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Mathematics
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oO_ƲRF_Oo
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14
What is the mean value of $|\sin x +\sin (\pi x)|$?
Jul 18, 2023
9
An attempt at generalizing a family of integrals $\int_0^{\alpha}{\frac{\sin \left( \pi x \right)}{x^x\left( \alpha -x \right) ^{\alpha -x}}}\, dx$
Feb 13, 2023
9
Evaluate $\int\limits_0^{\sqrt 2 } {\frac{1}{{3{a^2} + 2}}\frac{{\arctan \left( {\sqrt {{a^2} + 1} } \right)}}{{\sqrt {{a^2} + 1} }}da}$
Sep 5, 2023
8
Evaluating $\int^\infty_0 \frac{\tanh(x)}{x\cosh(2x)}dx$
Feb 10, 2023
7
Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$
Sep 14, 2023
5
Conjecture: $\,\lim\limits_{n\to\infty}\int_0^1 (1+|\sin{nx}|)^{-2}\mathrm dx=\frac{4}{3\pi}$
Jul 16, 2023
5
Tough integrals: $\int_0^1\frac{\log x\arctan\left(\frac{\log x}{2\pi}\right)}{1+x^2}dx$
Sep 15, 2023
5
Proving that $\int_{0}^{1}\left(\zeta(t)+\frac{1}{1-t}\right)dt=\sum_{n=0}^{\infty}\frac{\gamma_{n}}{(n+1)!}$
Nov 25, 2023
4
A conjecture involving series with zeta function
Aug 28, 2023
4
Compute ; $\Gamma=\lim_{n\to\infty} \int_{t_n}^{t_{n+1}} \frac{(f(x-t_n))^{g(t_{n+1}-x)}}{(f(t_{n+1}-x))^{g(x-t_n)}+(f(x-t_n))^{g(t_{n+1}-x)}} \, dx$
Jul 22, 2023