Compute $\int_0^\infty \frac{f(ax)-f(bx)}{x}dx.$
717
Proof of Frullani's theorem
112621
Finding $\int_{0}^{\infty} \frac{e^{3x}-e^x}{x(e^{3x}+1)(e^x+1)} dx$
69124
Integral $\int_{0}^{\infty}e^{-ax}\cos (bx)\operatorname d\!x$
23087
Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis
129734
Computing $\sum_{k=1}^{\infty}\frac{1}{k}\int_{\pi k}^{\infty}\frac{\sin(x)}{x}dx$
129892
show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
150809
Compute $ \int_0^1\frac{\ln^2(1+x)}{1+x^2}\, dx$
98710
Finding $\int_0^{\infty}xe^{-\lambda x} \, dx$
100180
Evaluate the integral $\int_0^\infty \frac{dx}{\sqrt{(x^3+a^3)(x^3+b^3)}}$
21375
The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$
84765
Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$
101587
Calculating $\int_{- \infty}^{\infty} \frac{\sin x \,dx}{x+i} $
81831
Evaluate $\int_0^{\infty}\frac{\log x}{1+e^x}\,dx$
59667
Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
10547
$\int_0^\infty \frac{\sin(x^2+ax)}{x}\,dx$ converges
15625
Computing $\int_0^\infty\mathrm{d} x\frac{x}{e^x+1}$ with contour integration
21390
How to integrate $\int_0^{\infty} \frac{e^{ax} - e^{bx}}{(1 + e^{ax})(1+ e^{bx})}dx$ where $a,b > 0$.