Calculate the integral $ F(a)=\int_{0}^{\infty} \frac{e^{-2x}-e^{ax}}{x} dx$
69348
Prove that $\int \limits _{0}^{\infty}\frac{e^{-2x}-e^{-ax}}{x}\text{d}x$ converges for any $a>0$
34967
Compute $ \int_{0}^{ \infty }\frac{\ln xdx}{x^{2}+ax+b}$
31792
show that $\int_{0}^{\infty}\frac{x\cos ax}{\sinh x}dx=\frac{\pi^2}{4} \operatorname{sech}^2 \left(\frac{a\pi}{2}\right) $
67622
Proving of Integral $\int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}dx = \ln\left(\frac{a}{b}\right)$
76129
Evaluate $\int_0^\infty\frac{\sin(\varphi_1x)}x\frac{\sin\varphi_2x}x\cdots\frac{\sin\varphi_nx}x\frac{\sin(ax)}x\cos(a_1x)\cdots\cos(a_mx) \, dx$
104138
How to integrate $\int\limits_0^\infty e^{-a x^2}\cos(b x) dx$ where $a>0$
105494
Gaussian-like integral : $\int_0^{\infty} e^{-x^2} \cos( a x) \ \mathrm{d}x$
4225
How to calculate $\int\limits_{-\infty}^\infty\frac{e^{ix}}{x}dx$
6014
Evaluating $\int_{-\infty}^{\infty}\frac{\exp\left(-a x^2\right)}{x^2+b^2}dx$
10070
Complex analysis: Calculating $\int_{-\infty}^{\infty} \frac{\sin x}{x} dx$ by using $f(z) = \frac{e^{iz} - 1}{iz}$
8642
Calculate $ \int_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}} dx $
57224
Compute $\int_0^\infty \frac{dx}{1+x^3}$
100194
Calculating $ \int _{0} ^{\infty} \frac{x^{3}}{e^{x}-1}\;dx$
123899
$\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$
49333
How to evaluate improper integral $\int_{0}^{\infty}\frac{\tan^{-1}{x}}{e^{ax}-1}dx$?
113066
Calculate $\int_0^1f(x)dx$
85081
$\int_{0}^{\infty} \frac{\cos x - e^{-x}}{x} \mathrm dx$ Evaluate Integral