How to computer $\int_0^1\log(\sin \pi x)\text{d}x$ under complex methods.
103598
Showing that $\int_0^1 \log(\sin \pi x)dx=-\log2$
11479
Integral yields log of holomorphic function
65407
Evaluating $\int\limits_0^\infty \frac{\log x} {(1+x^2)^2} dx$ with residue theory
79466
Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$
33729
Logarithm function of an arbitrary integer base in C
74241
Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
117751
An integral of a rational function of logarithm and nonlinear arguments
12604
Evaluate $\int_0^\pi xf(\sin x)dx$
23087
Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis
148613
Integrate $\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$
144811
Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
101045
Is there a closed form for the integral $\int_0^1 x^n \log^m (1-x) \, {\rm d}x$?
30829
A question in Complex Analysis $\int_0^{2\pi}\log(1-2r\cos x +r^2)\,dx$
18836
Complex integral over a circle
93610
What is $\int_0^1 \frac{\log \left(1-x^2\right) \sin ^{-1}(x)^2}{x^2} \, dx$?
54638
Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$
145183
finding $\int_0^\infty \dfrac{dx}{1+x^4}$ through complex analysis