Rigorously proving $\displaystyle\int^{\infty}_0 \frac{\sin{x}}{x} dx= \frac{\pi}{2}$
3704
Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
122301
Evaluating and proving $\lim\limits_{x\to\infty}\frac{\sin x}x$
129734
Computing $\sum_{k=1}^{\infty}\frac{1}{k}\int_{\pi k}^{\infty}\frac{\sin(x)}{x}dx$
79908
Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$
36701
$\displaystyle\int_{0}^{2\pi}\frac{1}{a+ \cos\theta}\,d\theta$
16775
Showing that $\int_{0}^{\infty} \frac{dx}{1 + x^2} = 2 \int_0^1 \frac{dx}{1 + x^2}$
65337
Compute $\int_{0}^{\infty}\frac{x\sin 2x}{9+x^{2}} \, dx$
4220
Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge?
137640
Proof that $\sum_{1}^{\infty} \frac{1}{n^2} <2$
124026
Prove $\int^\infty_0\frac x{e^x-1}dx=\frac{\pi^2}{6}$
63134
Showing $2\int_{-\infty}^{\infty} x f(x) F(x) \ dx = \frac{1}{\sqrt{\pi}}$ for standard normal pdf and cfd
60572
Computing $\int_{-\infty}^\infty \frac{\sin x}{x} \mathrm{d}x$ with residue calculus
64485
Proving $\displaystyle\lim_{h\to0}\frac{f(x+h)-2f(x)+f(x-h)}{h^2}=f''(x)$
109785
show that $\int_{0}^{\infty} \frac {\sin^3(x)}{x^3}dx=\frac{3\pi}{8}$
107296
How do I prove $\int_{-\infty}^{\infty}{\cos(x+a)\over (x+b)^2+1}dx={\pi\over e}{\cos(a-b)}$?
117264
Prove that $\int_0^{\infty} \frac{\sin x}{x^p}\, dx$ converges for $0<p<2$
81258
Evaluation of $\int_{-\infty}^\infty \frac{\sin(at)}t\ dt$