query: Evaluate $\int_{0}^{\pi} \log \left(m^2-2m\cos x+1\right)\: dx$
positive_passages.docid: 6483
positive_passages.text: Computing $\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right) \, dx$
negative_passages.docid: 26444
negative_passages.text: How can I integrate $\ln \left( x+\sqrt{1+x^2} \right) $?
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: 132369
negative_passages.text: Evaluating the indefinite integral $\int\log\!\left(x+\sqrt{x^2-1}\right)\!dx$
negative_passages.docid: 79466
negative_passages.text: Evaluating $\int_0^1 \log \log \left(\frac{1}{x}\right) \frac{dx}{1+x^2}$
negative_passages.docid: 5034
negative_passages.text: A closed form of $\int_0^1\frac{\ln\ln\left({1}/{x}\right)}{x^2-x+1}\mathrm dx$
negative_passages.docid: 80553
negative_passages.text: Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
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: 54638
negative_passages.text: Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$
negative_passages.docid: 40881
negative_passages.text: Evaluate $\int_{0}^{+\infty }{\left( \frac{x}{{{\text{e}}^{x}}-{{\text{e}}^{-x}}}-\frac{1}{2} \right)\frac{1}{{{x}^{2}}}\text{d}x}$
negative_passages.docid: 65407
negative_passages.text: Evaluating $\int\limits_0^\infty \frac{\log x} {(1+x^2)^2} dx$ with residue theory
negative_passages.docid: 137060
negative_passages.text: Evaluating $\int_0^{\tfrac{\pi}{4}}\ln(\cos x-\sin x)\ln(\cos x) dx - \int_0^{\tfrac{\pi}{4}}\ln(\cos x+\sin x)\ln(\sin x)dx=\frac{G\ln 2}{2}$
negative_passages.docid: 99753
negative_passages.text: How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?
negative_passages.docid: 91306
negative_passages.text: Integration of $\frac{1}{\log(x)}$
negative_passages.docid: 92637
negative_passages.text: Evaluating $\int \frac{\operatorname dx}{x\log x}$
negative_passages.docid: 130935
negative_passages.text: Evaluating $\int_{0}^{1}\frac{x-1}{(x+1)\ln x} dx $
negative_passages.docid: 142516
negative_passages.text: Evaluating the integral, $\int_{0}^{\infty} \ln\left(1 - e^{-x}\right) \,\mathrm dx $