Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
15324
A sine integral $\int_0^{\infty} \left(\frac{\sin x }{x }\right)^n\,\mathrm{d}x$
51837
Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$
117264
Prove that $\int_0^{\infty} \frac{\sin x}{x^p}\, dx$ converges for $0<p<2$
9730
Solve the integral $\int_0^\infty x/(x^3+1) dx$
24022
Compute $\int _0 ^{2\pi} (\sum_{n=1}^\infty \frac {\cos(nx)}{2^n})^2 dx$
13747
Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
21088
Prove $\int\limits_{0}^{\pi/2}\frac{dx}{1+\sin^2{(\tan{x})}}=\frac{\pi}{2\sqrt{2}}\bigl(\frac{e^2+3-2\sqrt{2}}{e^2-3+2\sqrt{2}}\bigr)$
53519
Finding $\int_0^1{\frac{x^4(1-x)^4}{1+x^2}}dx$
93174
Evaluate integral $\int_0^\pi \sin^4\left(x+\sin 3x\right)dx$
60559
How prove this $x^3<\sin^2{x}\tan{x},x\in\left(0,\dfrac{\pi}{2}\right)$
3704
Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
38511
Evaluation of $\int\frac{1}{x^2.(x^4+1)^{\frac{3}{4}}}dx$
8829
How to prove $\int_{-\infty}^{+\infty} f(x)dx = \int_{-\infty}^{+\infty} f\left(x - \frac{1}{x}\right)dx?$
147108
Prove that $\int_0^\infty \frac{x\,\log x}{(1+x^2)^2} = 0$
145019
Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$
72036
Closed form of $\int_0^\infty \sin(x)\sin\left(\frac{1}{x}\right)dx$?
21240
Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only