How to prove $\int_{0}^{\infty}\frac{e^{-\frac{x^2}{2}-\frac{z^2}{2x^2}}}{x^2}dx=\sqrt{\frac{\pi }{2}}\frac{ze^{-|z|}}{|z|}$?
137549
Given $\int_0^{\infty}e^{-x^2}dx = \frac{\sqrt{\pi}}{2}$, evaluate $\int_0^{\infty}e^{-a^2x^2-\frac{b^2}{x^2}}dx $
106812
Find $\int_{0}^{\infty} \frac{\ln(x)}{1+x^2}dx$
100711
$\int_{-\infty}^{\infty}e^{-zt^2 + 2wt} \ dt = e^{w^2 / z} \sqrt{\frac{\pi}{z}}$ for $z,w \in \mathbb{C}, Re(z) > 0$
129892
show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
30385
Proving that $\frac{e^x + e^{-x}}2 \le e^{x^2/2}$
51284
$\int_{-\infty}^\infty \frac{e^{ax}}{1+e^x}dx$ with residue calculus
77721
Is it possible to compute $\int_1^{+ \infty} \frac{dx}{x^2(1+e^x)}$?
114195
Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$
119410
Solution of $\int_0^\infty\frac{\ln(1+{x^2})}{1+{x^2}}$
109121
How to find integral of $\int_0^\infty \frac{\ln ^2z} {1+z^2}\mathrm{d}z$?
765
$\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues
35319
I'm looking for several ways to prove that $\int_{0}^{\infty }\sin(x)x^mdx=\cos(\frac{\pi m}{2})\Gamma (m+1)$
81621
How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$?
8934
How do I solve this improper integral: $\int_{-\infty}^\infty e^{-x^2-x}dx$?
85081
$\int_{0}^{\infty} \frac{\cos x - e^{-x}}{x} \mathrm dx$ Evaluate Integral
122843
Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$
93759
Evaluate $\int_{0}^{\infty} \frac{e^{ax}-e^{bx}}{(1+e^{ax})(1+e^{bx})} dx$