Evaluating $\int_{0}^{\infty} \frac {b \sin (ax) - a \sin (bx)}{x^2}dx$ for $a,b \gt 0$
717
Proof of Frullani's theorem
68097
Prove $\int\limits_{0}^{\infty} \mathrm{exp}(-ax^{2}-\frac{b}{x^{2}}) \mathrm{d} x = \frac{1}{2}\sqrt{\frac{\pi}{a}}\mathrm{e}^{-2\sqrt{ab}}$
36366
Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
83966
Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral?
6014
Evaluating $\int_{-\infty}^{\infty}\frac{\exp\left(-a x^2\right)}{x^2+b^2}dx$
58646
Are there any ways to evaluate $\int^\infty_0\frac{\sin x}{x}dx$ without using double integral?
114195
Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$
95426
How to compute $ \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \frac{e^{-{x^2}/{2}}}{1+e^{-(ax+b)}}\,\mathrm dx $ when $b \ne 0$
86712
Use rectangular contour to integrate $\int_{0}^{\infty}\frac{\sin(ax)}{e^{2\pi x}-1}dx$
153867
Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
3068
Evaluating $\int_0^\infty \sin x^2\, dx$ with real methods?
23087
Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis
108554
Integrating $\int_0^\infty\frac{1}{1+x^6}dx$
141892
How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$
129892
show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
101587
Calculating $\int_{- \infty}^{\infty} \frac{\sin x \,dx}{x+i} $
27002
Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$