Any easier way to do $\int^\infty_0 e^{-(x^2+\frac{\alpha^2}{x^2})\beta^2} = \frac{\sqrt{\pi}}{2\beta}e^{-2\alpha\beta^2}$
68097
Prove $\int\limits_{0}^{\infty} \mathrm{exp}(-ax^{2}-\frac{b}{x^{2}}) \mathrm{d} x = \frac{1}{2}\sqrt{\frac{\pi}{a}}\mathrm{e}^{-2\sqrt{ab}}$
108357
Integral $\int_0^\infty \log^2 x\frac{1+x^2}{1+x^4}dx=\frac{3 \pi^3}{16\sqrt 2}$
111775
$\int_{-\infty}^{+\infty} e^{-x^2} dx$ with complex analysis
89602
$ \int_{0}^{ \infty} \int_{0}^{ \infty} \frac { e^{-(x+y)}}{x+y} dx dy $
129892
show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
765
$\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues
48233
Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.
4287
Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$
42758
How to find $ \int_0^\infty \dfrac x{1+e^x}\ dx$
72039
Compute $\int_0^\infty\frac{\cos(xt)}{1+t^2}dt$
59667
Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
124445
Integral of the form $\int_{0}^{\infty}e^{-ax}e^{-x^{4}}dx$
100194
Calculating $ \int _{0} ^{\infty} \frac{x^{3}}{e^{x}-1}\;dx$
95426
How to compute $ \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \frac{e^{-{x^2}/{2}}}{1+e^{-(ax+b)}}\,\mathrm dx $ when $b \ne 0$
144039
Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$
7042
Defined integral of $x^{\alpha} (1-x)^{\beta-1}$
104904
Calculating $\int_0^\infty \frac {\sin^2x}{x^2}dx$ using the Residue Theorem.