Result of $\int \limits_{-\infty}^{+\infty}x^2\times\exp\left(\dfrac{-x^2}{2}\right)\mathrm{d}x$
94395
Integral: $\int_{-\infty}^{\infty} x^2 e^{-x^2}\mathrm dx$
57600
Show $\lim\limits_{a \rightarrow + \infty} \int_0^{\infty} \frac{1}{1+y^2}e^{-ay} dy =0 $
109901
Computing $\int_0^\infty\frac1{(x+1)(x+2)\cdots(x+n)}\mathrm dx $
4287
Proving $\int_{0}^{\infty} \mathrm{e}^{-x^2} dx = \frac{\sqrt \pi}{2}$
78008
A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$
177
How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$
70830
How to evaluate $\int_{0}^{\infty}\exp(-x^2-1/x^2)dx$?
68821
Prove $\int_0^{\infty} \left(\sqrt{1+x^{4}}-x^{2}\right)\ dx=\frac{\Gamma^{2}\left(\frac{1}{4}\right)}{6\sqrt{\pi}}$
136450
Compute $\lim_{x \rightarrow +\infty} \frac{[\int^x_0 e^{y^{2}} dy]^2}{\int^x_0 e^{2y^{2}}dy}$
117370
$\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} e^{-2n}$
45806
Finding $\lim\limits_{n \rightarrow \infty}\left(\int_0^1(f(x))^n\,\mathrm dx\right)^\frac{1}{n}$ for continuous $f:[0,1]\to[0,\infty)$
40227
Compute $\lim\limits_{n\to\infty}n^2\left(\left(1+\frac1{n+1}\right)^{n+1}-\left(1+\frac1n\right)^n\right)$
58475
Does $\int_0^\infty |\cos(x^2)| \mathrm dx$ converge?
68097
Prove $\int\limits_{0}^{\infty} \mathrm{exp}(-ax^{2}-\frac{b}{x^{2}}) \mathrm{d} x = \frac{1}{2}\sqrt{\frac{\pi}{a}}\mathrm{e}^{-2\sqrt{ab}}$
24974
Closed form for $\int_0^1\log\log\left(\frac{1}{x}+\sqrt{\frac{1}{x^2}-1}\right)\mathrm dx$
140386
Integrate $\int {\dfrac{x^2+\left(n-1\right)n}{\left(x\sin x+n\cos x\right)^2}}dx $
41434
Show that: $\lim \limits_{n \rightarrow+\infty} \int_{0}^{1}{f(x^n)dx}=f(0)$