Evaluate $ \int_0^\frac{\pi}{2}\frac{x\ln(1-\sin x)}{\sin x} dx$
34905
Proving that $\int_0^1 \frac{\arctan x}{x}\ln\left(\frac{1+x^2}{(1-x)^2}\right)dx=\frac{\pi^3}{16}$
117587
$\int_{0}^{1}\frac{\sin^{-1}\sqrt x}{x^2-x+1}dx$
55738
Evaluating $\int _0^{\frac{\pi }{2}}\:\frac{\sqrt[3]{\sin^2\left(x\right)}}{\sqrt[3]{\sin^2\left(x\right)}+\sqrt[3]{\cos^2\left(x\right)}}dx$
150809
Compute $ \int_0^1\frac{\ln^2(1+x)}{1+x^2}\, dx$
27002
Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
9653
Evaluate the integral $\int^{\frac{\pi}{2}}_0 \frac{\sin^3x}{\sin^3x+\cos^3x}\,\mathrm dx$.
118701
Evaluate $\int_{0}^{\frac{\pi }{2}}\frac{x dx}{\sin x +\cos x}$
67837
Evaluation of $\int_{0}^{1}\frac{x\ln (x)}{\sqrt{1-x^2}}dx$
102156
Integral of $\int_0^{\pi/2} \frac {\sqrt{\sin x}}{\sqrt {\sin x} + \sqrt {\cos x}}$dx
148613
Integrate $\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$
60182
Evaluate $\int\frac{1}{\sin(x-a)\sin(x-b)}\,dx$
12604
Evaluate $\int_0^\pi xf(\sin x)dx$
85814
Quotient of two integrals $\frac{\int_0^\pi x^3\ln(\sin x)\,dx}{\int_0^\pi x^2\ln(\sqrt{2}(\sin x))\,dx}$
98838
How to evaluate $\int_0^1 \frac{\ln(x+1)}{x^2+1} dx$
10341
complex integration $\frac{1-|a|^{2}}{\pi}\int_{L}\frac{|dz|}{{|z+a|}^{2}}$
74241
Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
79466
Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$