Show that $\int_{-\infty}^{\infty} \frac{1}{x^4 + 1} \,dx = \frac{\pi}{\sqrt{2}}$
48233
Evaluating $\int_0^\infty \frac{dx}{1+x^4}$.
147759
Integral $ \dfrac { \int_0^{\pi/2} (\sin x)^{\sqrt 2 + 1} dx} { \int_0^{\pi/2} (\sin x)^{\sqrt 2 - 1} dx} $
67263
Compute integral $\int_{-\infty}^\infty \frac{x^4}{1+x^8} \, dx$
126046
solving the integral $ \int_0^\infty \dfrac{\sin xt}{x(x^2+1)} dx $
108357
Integral $\int_0^\infty \log^2 x\frac{1+x^2}{1+x^4}dx=\frac{3 \pi^3}{16\sqrt 2}$
151649
Exact Values of the integal $\int_0^\infty \frac{r^{n-1}}{(1+r^2)^{\frac{s}{2}}}\,dr$
45205
Showing that $\int_0^\infty x^{-x} \mathrm{d}x \leq 2$.
83325
Integral of $\frac{\sqrt{x^2+1}}{x}$
95426
How to compute $ \frac{1}{\sqrt{2\pi}} \int_{-\infty}^\infty \frac{e^{-{x^2}/{2}}}{1+e^{-(ax+b)}}\,\mathrm dx $ when $b \ne 0$
137549
Given $\int_0^{\infty}e^{-x^2}dx = \frac{\sqrt{\pi}}{2}$, evaluate $\int_0^{\infty}e^{-a^2x^2-\frac{b^2}{x^2}}dx $
101587
Calculating $\int_{- \infty}^{\infty} \frac{\sin x \,dx}{x+i} $
129734
Computing $\sum_{k=1}^{\infty}\frac{1}{k}\int_{\pi k}^{\infty}\frac{\sin(x)}{x}dx$
109901
Computing $\int_0^\infty\frac1{(x+1)(x+2)\cdots(x+n)}\mathrm dx $
69978
Evaluating $\int_1^\infty \frac{1}{x(x^2+1)}\ dx$
4287
Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$
75423
Computing $\int_0^\infty\frac{1}{(1+x^{2015})(1+x^2)}$
51837
Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$