query: Solving the integral $\int_{0}^{\pi}{\log(\sin x)}\,\mathrm dx$
positive_passages.docid: 158279
positive_passages.text: $\int_0^{\pi/2}\ln(\sin(x))$?
negative_passages.docid: 125523
negative_passages.text: How to find $\int_{0}^{\pi/2} \log ({1+\cos x}) dx$ using real-variable methods?
negative_passages.docid: 140669
negative_passages.text: Evaluating the log gamma integral $\int_{0}^{z} \log \Gamma (x) \, \mathrm dx$ in terms of the Hurwitz zeta function
negative_passages.docid: 88154
negative_passages.text: Proving $\int_{0}^1\frac{x-1}{\log x}dx=\log 2$ and $\int_{0}^1\frac{\log x}{x-1}dx=\frac{\pi^2}{6}$
negative_passages.docid: 6892
negative_passages.text: Why is it not true that $\int_0^{\pi} \sin(x)\; dx = 0$?
negative_passages.docid: 74822
negative_passages.text: How to evaluate $\int_{0}^{\pi }\theta \ln\tan\frac{\theta }{2} \, \mathrm{d}\theta$
negative_passages.docid: 118324
negative_passages.text: Other challenging logarithmic integral $\int_0^1 \frac{\log^2(x)\log(1-x)\log(1+x)}{x}dx$
negative_passages.docid: 34855
negative_passages.text: Evaluate the integral: $\int_{0}^{1} \frac{\ln(x+1)}{x^2+1} \mathrm dx$
negative_passages.docid: 54638
negative_passages.text: Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$
negative_passages.docid: 135519
negative_passages.text: How to approach solving $\int_0^{\pi/2} \ln(a^2 \cos^2 x +b^2 \sin^2 x ) dx$
negative_passages.docid: 109316
negative_passages.text: How to calculate $\int_0^{\pi/2} \sin^a x \cos^b x \,\mathrm{d} x$
negative_passages.docid: 63650
negative_passages.text: Evaluating the contour integral $\int_{0}^{\infty}\frac{\sin^{3}(x)}{x^{3}}\mathrm dx$
negative_passages.docid: 24182
negative_passages.text: Evaluating $\int_{0}^{\infty}\frac{\sin^{2n+1}x}{x}\mathrm{d}x$
negative_passages.docid: 135653
negative_passages.text: An integral$\frac{1}{2\pi}\int_0^{2\pi}\log|\exp(i\theta)-a|\text{d}\theta=0$ which I can calculate but can't understand it.
negative_passages.docid: 153867
negative_passages.text: Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
negative_passages.docid: 48408
negative_passages.text: Definite Integral of $\sin(\sin x)$
negative_passages.docid: 26608
negative_passages.text: How to show that $\int_{0}^{\pi}{\sin^5 x\over 1+\cos^3 x}\mathrm dx=\ln 3?$