Index
stringlengths
1
5
Challenge
stringlengths
41
1.55k
Answer in Latex
stringclasses
122 values
Answer in Sympy
stringlengths
1
774
Variation
stringclasses
31 values
Source
stringclasses
61 values
401
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(9997025\right) n \cdot ( \left(3399363\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(8635398\right) n \cdot ( \left(3399363\right) x)^n\right$
Sum(n*x**n*(n**2 - 1)*3399363**n, (n, 2, oo))*8635398*9997025/6
Numeric-All-7
U-Math sequences_series fb6418ae-3440-4258-9388-89d799fd859a
402
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(50849136\right) n \cdot ( \left(49317708\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(38518091\right) n \cdot ( \left(49317708\right) x)^n\right$
Sum(n*x**n*(n**2 - 1)*49317708**n, (n, 2, oo))*38518091*50849136/6
Numeric-All-8
U-Math sequences_series fb6418ae-3440-4258-9388-89d799fd859a
403
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(597140185\right) n \cdot ( \left(908557767\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(130111075\right) n \cdot ( \left(908557767\right) x)^n\right$
Sum(n*x**n*(n**2 - 1)*908557767**n, (n, 2, oo))*130111075*597140185/6
Numeric-All-9
U-Math sequences_series fb6418ae-3440-4258-9388-89d799fd859a
404
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( \left(7136646496\right) n \cdot ( \left(3240980819\right) x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( \left(3618373856\right) n \cdot ( \left(3240980819\right) x)^n\right$
Sum(n*x**n*(n**2 - 1)*3240980819**n, (n, 2, oo))*3618373856*7136646496/6
Numeric-All-10
U-Math sequences_series fb6418ae-3440-4258-9388-89d799fd859a
405
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot (F x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left(B n \cdot (F x)^n\right$
B*Sum(F**n*n*x**n*(n**2 - 1), (n, 2, oo))/6
Symbolic-2
U-Math sequences_series fb6418ae-3440-4258-9388-89d799fd859a
406
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left(A n \cdot (F x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot (F x)^n\right$
A*Sum(F**n*n*x**n*(n**2 - 1), (n, 2, oo))/6
Symbolic-2
U-Math sequences_series fb6418ae-3440-4258-9388-89d799fd859a
407
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left(A n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left(B n \cdot ( x)^n\right$
A*B*Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6
Symbolic-2
U-Math sequences_series fb6418ae-3440-4258-9388-89d799fd859a
408
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot (F x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot (F x)^n\right$
Sum(F**n*n*x**n*(n**2 - 1), (n, 2, oo))/6
Symbolic-1
U-Math sequences_series fb6418ae-3440-4258-9388-89d799fd859a
409
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left(B n \cdot ( x)^n\right$
B*Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6
Symbolic-1
U-Math sequences_series fb6418ae-3440-4258-9388-89d799fd859a
410
Find the (infinite) power series of $f(x) \cdot g(x)$ for given $f(x) = \sum_{n=1}^\infty \left(A n \cdot ( x)^n\right)$ and $g(x) = \sum_{n=1}^\infty \left( n \cdot ( x)^n\right$
A*Sum(n*x**n*(n**2 - 1), (n, 2, oo))/6
Symbolic-1
U-Math sequences_series fb6418ae-3440-4258-9388-89d799fd859a
411
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
412
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
413
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
414
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
415
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
416
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
417
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
418
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
419
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
420
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
421
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
422
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
423
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
424
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
425
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
426
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
427
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
428
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
429
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
430
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
431
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
432
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
433
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\sin^{2}{\left(- A x \right)} + \cos^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
434
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(A - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(A - 1\right) \right)} + 1\right) \tan{\left(A x \right)}}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
435
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
436
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
437
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
438
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
439
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
440
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
441
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
442
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
443
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
444
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
445
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
446
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
447
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
448
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
449
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
450
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
451
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
452
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
453
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
454
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
455
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
456
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
457
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(- \sinh^{2}{\left(A x \right)} + \cosh^{2}{\left(A x \right)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
458
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\sinh{\left(\log{\left(A x + \sqrt{A^{2} x^{2} + 1} \right)} \right)}}{A x}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
459
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
460
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
461
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
462
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
463
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
464
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
465
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
466
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
467
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
468
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
469
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
470
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
471
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
472
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
473
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
474
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
475
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{2^{- N} x}{B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
476
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(\frac{B \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} B}}{x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
477
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
478
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
479
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
480
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
481
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{2^{- N} x}{F}}{x}\right) \left(\sin( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\ln(x) \cdot \log_{x}(A)}{\ln(A)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{i \left(e^{i B x} - e^{- i B x}\right)}{2 \sin{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
482
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{F \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} F}}{x}\right) \left(\sin( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \cos\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{\log_A\left(\frac{x}{e}\right) + \log_A(e)}{\log_A(x)}\right) x) \cdot \sin\left(\frac{ \left(- \frac{2 i \left(e^{4 i B x} + 1\right) \tan{\left(B x \right)}}{\left(1 - e^{4 i B x}\right) \left(1 - \tan^{2}{\left(B x \right)}\right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
483
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
484
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
485
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
486
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
487
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\sin^{2}{\left(- B x \right)} + \cos^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
488
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(B - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(B - 1\right) \right)} + 1\right) \tan{\left(B x \right)}}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
489
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
490
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
491
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\ln(x) \cdot \log_{x}(F)}{\ln(F)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
492
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\log_F\left(\frac{x}{e}\right) + \log_F(e)}{\log_F(x)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
493
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(- \sinh^{2}{\left(B x \right)} + \cosh^{2}{\left(B x \right)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
494
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\sinh{\left(\log{\left(B x + \sqrt{B^{2} x^{2} + 1} \right)} \right)}}{B x}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
495
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\sin^{2}{\left(- F x \right)} + \cos^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
496
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\tan{\left(x \right)} + \tan{\left(x \left(F - 1\right) \right)}}{\left(- \tan{\left(x \right)} \tan{\left(x \left(F - 1\right) \right)} + 1\right) \tan{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
497
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \sinh^{2}{\left(F x \right)} + \cosh^{2}{\left(F x \right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
498
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(\frac{\sinh{\left(\log{\left(F x + \sqrt{F^{2} x^{2} + 1} \right)} \right)}}{F x}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
499
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{i \left(e^{i F x} - e^{- i F x}\right)}{2 \sin{\left(F x \right)}}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{2^{- N} x}{A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\ln(x) \cdot \log_{x}(B)}{\ln(B)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Easy
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921
500
Compute the first 6 nonzero terms of the Maclaurin series of $f(x) = \left(- \frac{2 i \left(e^{4 i F x} + 1\right) \tan{\left(F x \right)}}{\left(1 - e^{4 i F x}\right) \left(1 - \tan^{2}{\left(F x \right)}\right)}\right) \left(\sin( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \cos\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right) + \cos( \left(\frac{A \sum_{N=1}^{\infty} \frac{6 x}{\pi^{2} N^{2} A}}{x}\right) x) \cdot \sin\left(\frac{ \left(\frac{\log_B\left(\frac{x}{e}\right) + \log_B(e)}{\log_B(x)}\right) \pi }{ 4 }\right)\right)$
sqrt(2)*x**5/240 + sqrt(2)*x**4/48 - sqrt(2)*x**3/12 - sqrt(2)*x**2/4 + sqrt(2)*x/2 + sqrt(2)/2
Equivalence-All-Hard
U-Math sequences_series f89bd354-18c9-4f31-b91f-cf6421e24921