How to show $\int_{0}^{\infty} \frac{dx}{x^3+1} = \frac{2\pi}{3\sqrt{3}}$
5537
Closed form for $ \int_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$
147479
Evaluate $\int \frac{2-3x}{2+3x}\sqrt\frac{1+x}{1-x}dx$
148743
$\int_0^\infty \frac{1}{1+x^ 9} \, dx$
84765
Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$
89602
$ \int_{0}^{ \infty} \int_{0}^{ \infty} \frac { e^{-(x+y)}}{x+y} dx dy $
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) $
123694
How to compute the integral $\int_{0}^{\infty} \frac{x^{1/3}}{1+x^{2}} \ dx$
76400
Finding $\int^{\infty}_{0}\frac{\ln^2(x)}{(1-x^2)^2} dx$
13287
Let $\int_{- \infty}^{\infty} f(x) dx =1$. Then show that $ \int_{- \infty}^{\infty} \frac{1}{1+ f(x)} dx = \infty.$
124026
Prove $\int^\infty_0\frac x{e^x-1}dx=\frac{\pi^2}{6}$
61133
Show that $\int|f(x)|dx=\int_0^\infty m(E_\alpha)d\alpha$
51837
Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$
4971
$\int_{0}^{1}\frac{1-x}{1+x}.\frac{dx}{\sqrt{x+x^2+x^3}}$
141688
Indefinite integral of $ \int \frac{x^3}{\sqrt{x^2+1}} \,\text{d}x$.
74955
Simplify result of $\int_0^{\infty} \frac{1}{1+x^n}dx$
62109
$\int_{-\infty}^{\infty} \frac{\cos(αx)}{(x^2+1)(x^2+4)} \mathrm dx$ using Complex methods
100569
Evaluating the improper integral $\int_{0}^{\infty} \frac{x^3}{e^{x}-1} dx$