What is $\int_0^{\frac{\pi}2}\ln(\sin x)dx$?
54638
Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$
6571
A Challenging Integral $\int_0^{\frac{\pi}{2}}\log \left( x^2+\log^2(\cos x)\right)dx$
64480
How do I find $\int_{0}^{\infty} \frac{\sin^4 x}{x^2}\,dx$?
30829
A question in Complex Analysis $\int_0^{2\pi}\log(1-2r\cos x +r^2)\,dx$
3704
Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
93071
Is there a way to calculate the improper integral $\int_0^\infty \big(\frac{\ln x}{x - 1}\big)^2 dx$?
27002
Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
121071
Calculation of $\int^{\pi/2}_{0}\cos^{n}(x)\cos (nx)\,dx$, where $n\in \mathbb{N}$
57686
Finding $ \int^1_0 \frac{\ln(1+x)}{x}dx$
137060
Evaluating $\int_0^{\tfrac{\pi}{4}}\ln(\cos x-\sin x)\ln(\cos x) dx - \int_0^{\tfrac{\pi}{4}}\ln(\cos x+\sin x)\ln(\sin x)dx=\frac{G\ln 2}{2}$
87242
Ways to prove $ \int_0^\pi dx \frac{\sin^2(n x)}{\sin^2 x} = n\pi$
148613
Integrate $\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$
132452
Integral $\int_{\frac{1}{2}}^1 \frac{\ln x}{\sqrt{x^2+1}}dx$
102639
How to receive the result of the integral $ \int\frac{1}{x}dx$ is $\ln|x|$?
146349
$\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
135447
Compute the integral $\int_0^{\frac\pi2}\frac{\mathrm d \theta}{\sqrt{\sin \theta}}$
30731
Integral ${\frac{1}{\pi^2}} \int_{0}^{\infty}\frac{{(\ln{x}})^2}{\sqrt{x}{(1-x)^2}} \mathrm d x$