query: Evaluate $\int_0^{2\pi}\ln(1+a^2-2a\cos(x))dx\text{ ,with }a>0$
positive_passages.docid: 6483
positive_passages.text: Computing $\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right) \, dx$
negative_passages.docid: 67837
negative_passages.text: Evaluation of $\int_{0}^{1}\frac{x\ln (x)}{\sqrt{1-x^2}}dx$
negative_passages.docid: 130935
negative_passages.text: Evaluating $\int_{0}^{1}\frac{x-1}{(x+1)\ln x} dx $
negative_passages.docid: 27195
negative_passages.text: Evaluating $\int_{0}^{1}\frac{1-x}{1+x}\frac{\mathrm dx}{\ln x}$
negative_passages.docid: 158279
negative_passages.text: $\int_0^{\pi/2}\ln(\sin(x))$?
negative_passages.docid: 9518
negative_passages.text: Evaluate: $ \int_0^1 \int_y^1 e^{x^2 }dxdy$
negative_passages.docid: 85949
negative_passages.text: Integral involving logarithm: $\int_0^\infty \frac{ \ln x}{(x+a)(x+b)} dx$
negative_passages.docid: 139121
negative_passages.text: Evaluating $\int _0 ^1 x^k(\ln x)^m dx$ for integer $k$ and $m$
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: 89499
negative_passages.text: Evaluating the integral $\int_0^{\frac{\pi}{2}}\log\left(\frac{1+a\cos(x)}{1-a\cos(x)}\right)\frac{1}{\cos(x)}dx$
negative_passages.docid: 6571
negative_passages.text: A Challenging Integral $\int_0^{\frac{\pi}{2}}\log \left( x^2+\log^2(\cos x)\right)dx$
negative_passages.docid: 74241
negative_passages.text: Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
negative_passages.docid: 95933
negative_passages.text: How to evaluate the integral $\int_0^{\pi}\frac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx$?
negative_passages.docid: 132388
negative_passages.text: Calculate $I=\int_0^1\frac{\ln(1+x)}{1+x^2}\,dx$
negative_passages.docid: 90313
negative_passages.text: Integrate $\int_0^\pi{{x\sin x}\over{1+\cos^2x}}dx$.
negative_passages.docid: 105860
negative_passages.text: Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
negative_passages.docid: 25509
negative_passages.text: evaluation of an integral involving algebraic numbers