Show that $\int^{\infty}_0 \frac{\sin^4 x}{x^4}=\frac{\pi} 3$.
36366
Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
107296
How do I prove $\int_{-\infty}^{\infty}{\cos(x+a)\over (x+b)^2+1}dx={\pi\over e}{\cos(a-b)}$?
129892
show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
101587
Calculating $\int_{- \infty}^{\infty} \frac{\sin x \,dx}{x+i} $
5537
Closed form for $ \int_0^\infty {\frac{{{x^n}}}{{1 + {x^m}}}dx }$
21088
Prove $\int\limits_{0}^{\pi/2}\frac{dx}{1+\sin^2{(\tan{x})}}=\frac{\pi}{2\sqrt{2}}\bigl(\frac{e^2+3-2\sqrt{2}}{e^2-3+2\sqrt{2}}\bigr)$
96191
Integral $\int_0^{\infty} \sin(x^2)/x^2\,dx$
129734
Computing $\sum_{k=1}^{\infty}\frac{1}{k}\int_{\pi k}^{\infty}\frac{\sin(x)}{x}dx$
151127
Confirm that $\int_{0}^{\infty}t^{-1}\sin t dt=\pi/2$
10675
Proving that $\frac{1}{2\pi}\int_{0}^{2\pi}|f(re^{it})|^2dt=\sum_{n=0}^{\infty}|a_n|^2r^{2n}$
144039
Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$
301
Prove: $\int_0^\infty \sin (x^2) \, dx$ converges.
11499
How to show the inequality for $\int_{0}^{\pi/4}\tan^n(x) dx$
50509
Prove that $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}}~dx=0$ (without trigonometric substitution)
11757
How can I compute the integral $\int_{0}^{\infty} \frac{dt}{1+t^4}$?
28771
Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $
100194
Calculating $ \int _{0} ^{\infty} \frac{x^{3}}{e^{x}-1}\;dx$