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19
Integral $\int_0^\infty\frac{dx}{\sqrt{1+\exp\left(\frac\pi2\left(x^2-\frac1{x^2}\right)\right) }}=\sqrt{\frac\pi2}$
math.stackexchange.com
11
Evaluate the Integral $\int_{0}^{\infty}\ln\left(1+\pi\frac{2\cosh\left(t\right)+\pi}{t^{2}+\cosh\left(t\right)^{2}}\right)dt$
math.stackexchange.com
10
Prove that $\int_0^\infty \frac{1+2\cos x+x\sin x}{1+2x\sin x +x^2}dx=\frac{\pi}{1+\Omega}$ where $\Omega e^\Omega=1$
math.stackexchange.com
10
For $n\ge m\ge 1$, how far can we walk with $ \int_0^{\frac{\pi}{2}} \frac{x^n}{\sin^m x} d x$?
math.stackexchange.com
9
$ \int_{-\infty}^{\infty}\frac{-1}{T}\frac{1}{2(\cosh(\omega/T)+1)}\sqrt{\frac{1+\sqrt{1+(\omega/\Delta)^{2}}}{1+(\omega/\Delta)^{2}}}d\omega$
math.stackexchange.com
8
Derivation of an integral containing the complete elliptic integral of the first kind
math.stackexchange.com
8
Proving a closed form for $\int_0^\pi \frac{\sin^{2n}x}{(1 - 2r\cos x + r^2)^{n+1}} \, dx$
math.stackexchange.com
8
Conjecture: If $x_k$ are random in $(0,\pi/2)$ then expectation of $\frac{\prod_{k=1}^n\tan x_k}{\sum_{k=1}^n\tan x_k}$ is $(\pi/2)^{2n-6}$ for $n>2$.
math.stackexchange.com
6
Evaluate $\int_{0}^{1}\int_{0}^{1}\int_{0}^{1}\sqrt{x^2+y^2+z^2}\arctan{\sqrt{x^2+y^2+z^2}}dxdydz$
math.stackexchange.com
6
Calculating $\int_0^{\infty } \left(\text{Li}_2\left(-\frac{1}{x^2}\right)\right)^2 \, dx$
math.stackexchange.com
6
Integral $\int_0^\infty\frac{\cos(\pi x^2)}{\cosh (\pi x)(\cosh (4\pi)-\cos(4\pi x))}dx$
math.stackexchange.com
6
Integrating $\int_0^{\pi/2}{x^2}\ln^2(\sin x)\ln(\cos x)dx$ and $\int_0^{\pi/2}x\ln(\sin x)\ln^2(\cos x)dx$
math.stackexchange.com
6
Closed form: show that $\sum_{n=1}^\infty\frac{a_n}{(n+1)4^n}=\zeta(2) $
math.stackexchange.com
5
Proving that $\int_0^1 \frac{\arctan x}{x}\ln\left(\frac{1+x^2}{(1-x)^2}\right)dx=\frac{\pi^3}{16}$
math.stackexchange.com