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Mathematics
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OnTheWay
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15
Convert integral $\int_0^{\frac{\sqrt3}2} {\frac{1}{{{x^{3/4}}{{\left( {1 + x} \right)}^{3/4}}}}dx}$ to elliptic integral
Jun 29, 2023
10
Without superior math, can we evaluate this limit?
Oct 22, 2021
8
Evaluate $\int_{0}^{1}\int_{0}^{1}\int_{0}^{1}\sqrt{x^2+y^2+z^2}\arctan{\sqrt{x^2+y^2+z^2}}dxdydz$
Feb 11, 2022
8
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 4, 2023
8
Evaluate the integral $\int\limits_0^\infty {{{\left( {\frac{e}{x}} \right)}^x}\Gamma \left( x \right)\sin \left( {2\pi x} \right)dx}$
Apr 30, 2023
7
How to evaluate $\sum_{k=1}^{\infty}\frac{B\left(k, \frac{1}{2}\right)}{(2k+1)^2}$, where $B(x, y)$ is the Beta function?
Apr 3, 2022
7
Two hard integrals: $\int_{0}^{1}\frac{\log{(x)}\log{(1-x)}\log{(1+x^2)}}{x}dx$ and $\int_{0}^{1}\frac{\log^2{(x)}\log{(1+x^2)}}{1-x}dx$
Jul 19, 2022
7
Evaluate the integral $\int\limits_{\frac{1}{3}}^{\frac{1}{2}} {\frac{{\ln \left( {1 - x} \right)\ln \left( {1 - 2x} \right)}}{x}dx} $
Aug 7, 2023
7
Sum with reciprocal central binomial and harmonic number $\sum_{n=1}^{\infty}\frac{H_{2n}}{n^2 C_{2n}^{n}}$
May 28, 2023
7
Proving $\sum_{k=1}^{2n-1}\frac{\sin(\frac{\pi k^2}{2n})}{\sin(\frac{\pi k}{2n})}=n$
Mar 16, 2023