Computing the integration $\int_0^{+\infty}{\frac{\sin(x)}{\sqrt{x}}}dx$.
13747
Proof of $\int_0^\infty \frac{\sin x}{\sqrt{x}}dx=\sqrt{\frac{\pi}{2}}$
123899
$\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$
156231
Computing $\lim\limits_{n\to\infty} \int_{0}^{\infty}\frac{\sin(x/n)}{(1+x/n)^{n}}\, dx$
100485
How do I evaluate the integral $\int_0^{\infty}\frac{x^5\sin(x)}{(1+x^2)^3}dx$?
31964
Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$
75423
Computing $\int_0^\infty\frac{1}{(1+x^{2015})(1+x^2)}$
117587
$\int_{0}^{1}\frac{\sin^{-1}\sqrt x}{x^2-x+1}dx$
67340
Integrate $\int \frac{dx}{\sqrt{\sin^3x\sin(x+\alpha)}}$
90313
Integrate $\int_0^\pi{{x\sin x}\over{1+\cos^2x}}dx$.
27002
Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
148613
Integrate $\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$
13978
Calculating the integral $\int_0^\infty \frac{\cos x}{1+x^2}\, \mathrm{d}x$ without using complex analysis
122843
Finding $\int_0^\infty \frac{\cos(ax)-\cos(bx)}{x}dx$
11757
How can I compute the integral $\int_{0}^{\infty} \frac{dt}{1+t^4}$?
60572
Computing $\int_{-\infty}^\infty \frac{\sin x}{x} \mathrm{d}x$ with residue calculus
144039
Computing $ \int_0^{\infty} \frac{ \sqrt [3] {x+1}-\sqrt [3] {x}}{\sqrt{x}} \mathrm dx$
29383
Computing $\int_{-\infty}^{\infty} \frac{\cos x}{x^{2} + a^{2}}dx$ using residue calculus