Why $\int_0^\infty e^{-t}\log tdt =-\gamma$?
40019
Showing that $\gamma = -\int_0^{\infty} e^{-t} \log t \,dt$, where $\gamma$ is the Euler-Mascheroni constant.
84413
Why is $\int_{-\infty}^\infty |g(x)|\,dx = \int_0^\infty \mu(\{x : |g(x)| \ge t\})\,dt$ true?
105494
Gaussian-like integral : $\int_0^{\infty} e^{-x^2} \cos( a x) \ \mathrm{d}x$
40564
Prove that $u(x,t)=\int_{-\infty}^{\infty}c(w)e^{-iwx}e^{-kw^2t}dw\rightarrow 0$ if $x\rightarrow \infty$
58456
Why is $ 1^{\infty} \not= \lim_{t \to \infty} 1^t = 1$?
19716
What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$?
102399
Computing $ \int_0^\infty \frac{\log x}{\exp x} \ dx $
123899
$\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$
119477
Understanding the Definition of $\int_\gamma f\ \overline{dz}$
61515
Evaluate $\int_0^{\infty} \frac{\log(x)dx}{x^2+a^2}$ using contour integration
81057
Evaluation of $\int_{\frac{1}{e}}^{\tan x}\frac{t}{1+t^2}dt+\int_{\frac{1}{e}}^{\cot x}\frac{1}{t(1+t^2)}dt$
113094
What is the integral of the gamma function
27347
Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.
48651
Prove that $\int_0^1t^{p-1}(1-t)^{q-1}\,dt=\frac{\Gamma(p)\Gamma(q)}{\Gamma(p+q)}$ for positive $p$ and $q$
121310
Integral $\int_0^1 \log \left(\Gamma\left(x+\alpha\right)\right)\,{\rm d}x=\frac{\log\left( 2 \pi\right)}{2}+\alpha \log\left(\alpha\right) -\alpha$
24716
$\int_0^\infty\frac{\log x dx}{x^2-1}$ with a hint.
16639
How to integrate $ \int_0^\infty \sin x \cdot x ^{-1/3} dx$ (using Gamma function)