For $n \in \mathbb{N}$, prove that $\int_{0}^{\infty}x^{n}e^{-x}dx=n!$
89028
Evaluate the integral $\int e^{-x}x^n dx$
40537
How to prove $\int_0^\infty e^{-x^2}cos(2bx) dx = \frac{\sqrt{\pi}}{2} e^{-b^2}$
64571
Prove that $\int_{E}f =\lim \int_{E}f_{n}$
36366
Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
32823
Prove $\forall n \in \mathbb{N}: \int_{0}^{\frac{\pi}{2}} |\frac{\sin(nx)}{x}|dx \geq \frac{2}{\pi}\sum_{k=1}^{n}\frac{1}{k}$
68097
Prove $\int\limits_{0}^{\infty} \mathrm{exp}(-ax^{2}-\frac{b}{x^{2}}) \mathrm{d} x = \frac{1}{2}\sqrt{\frac{\pi}{a}}\mathrm{e}^{-2\sqrt{ab}}$
5229
Prove that $\lim_{n \to \infty} \int_0^1{nx^nf(x)}dx$ is equal to $f(1)$.
61659
How to show that $ \sum_{n = 0}^{\infty} \frac {1}{n!} = e$?
148743
$\int_0^\infty \frac{1}{1+x^ 9} \, dx$
88690
$\int_a^b f(x)\mathrm dx=0$ for all $-\infty<a<b<\infty$ a,b rational implies $f=0$ a.e
25652
Intuitive explanation for $\mathbb{E}X= \int_0^\infty 1-F(x) \, dx$
70746
Proving that $(x_n)_{n=1}^{\infty}$ is a Cauchy sequence.
37015
Prove $\int_X |f|^p=p\int^{\infty}_{0} t^{p-1}\mu({x: |f(x)>t}) dt\,$
122820
Prove $\lim_{n\to\infty}x_n=2$ Given $\lim_{n \to \infty} x_n^{x_n} = 4$
34308
Given $|z|<1$ prove $\lim_{n \to \infty} z^n=0$.
40564
Prove that $u(x,t)=\int_{-\infty}^{\infty}c(w)e^{-iwx}e^{-kw^2t}dw\rightarrow 0$ if $x\rightarrow \infty$
135380
Show that $\sum_{n=1}^\infty \frac{n^2}{(n+1)!}=e-1$