$\int_0^{\infty} \frac{\sin(x)}{ \sqrt{x}}dx$
13747
Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
65337
Compute $\int_{0}^{\infty}\frac{x\sin 2x}{9+x^{2}} \, dx$
146349
$\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
147759
Integral $ \dfrac { \int_0^{\pi/2} (\sin x)^{\sqrt 2 + 1} dx} { \int_0^{\pi/2} (\sin x)^{\sqrt 2 - 1} dx} $
76129
Evaluate $\int_0^\infty\frac{\sin(\varphi_1x)}x\frac{\sin\varphi_2x}x\cdots\frac{\sin\varphi_nx}x\frac{\sin(ax)}x\cos(a_1x)\cdots\cos(a_mx) \, dx$
15569
Integral of the form $\int_0^\infty \exp{\left(-\frac{(a+bx)^2}{x}\right)}\frac{dx}{\sqrt{x^3}}$
10547
$\int_0^\infty \frac{\sin(x^2+ax)}{x}\,dx$ converges
36366
Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$
27002
Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
102156
Integral of $\int_0^{\pi/2} \frac {\sqrt{\sin x}}{\sqrt {\sin x} + \sqrt {\cos x}}$dx
35861
Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
83966
Does $ \int_0^{\infty}\frac{\sin x}{x}dx $ have an improper Riemann integral or a Lebesgue integral?
91290
Evaluating $\lim_{n \to \infty} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^2(nx)} dx$
141892
How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$
148613
Integrate $\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$
108554
Integrating $\int_0^\infty\frac{1}{1+x^6}dx$
67340
Integrate $\int \frac{dx}{\sqrt{\sin^3x\sin(x+\alpha)}}$