query: How to integrate $\frac{1}{(1+a\cos x)}$ from $-\pi$ to $\pi$
positive_passages.docid: 27910
positive_passages.text: How to evaluate $\int_0^{2\pi} \frac{d\theta}{A+B\cos\theta}$?
negative_passages.docid: 6483
negative_passages.text: Computing $\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right) \, dx$
negative_passages.docid: 6852
negative_passages.text: Integral of $\int \frac{x \sin{x} \cos{x}}{(a^2 \sin^2 x + b^2 \cos^2 x)^2} dx $
negative_passages.docid: 118701
negative_passages.text: Evaluate $\int_{0}^{\frac{\pi }{2}}\frac{x dx}{\sin x +\cos x}$
negative_passages.docid: 95068
negative_passages.text: Integral of $\frac{1}{2x}$
negative_passages.docid: 36586
negative_passages.text: Evaluating $\frac{1}{2\pi}\int_{0}^{2\pi}\frac{1}{1-2t\cos\theta +t^2}d\theta$
negative_passages.docid: 109416
negative_passages.text: How to calculate $\int_0^1 \frac{\ln(1-x)}{x} dx$?
negative_passages.docid: 115759
negative_passages.text: Evaluating this integral : $ \int \frac {1-7\cos^2x} {\sin^7x \cos^2x} dx $
negative_passages.docid: 24832
negative_passages.text: Integrating $\frac{1}{\sqrt{ax^2+bx+c}}$ for $a<0$
negative_passages.docid: 105765
negative_passages.text: Integrating $\frac{x^k }{1+\cosh(x)}$
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: 31529
negative_passages.text: Integrating $\int^2_{-2}\frac{x^2}{1+5^x}$
negative_passages.docid: 126576
negative_passages.text: Most efficient way to integrate $\int_0^\pi \sqrt{4\sin^2 x - 4\sin x + 1}\,dx$?
negative_passages.docid: 90185
negative_passages.text: Another way to evaluate $\int\frac{\cos5x+\cos4x}{1-2\cos3x}{dx}$?
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: 119669
negative_passages.text: Evaluate $\int \frac{1}{\sin x\cos x} dx $
negative_passages.docid: 15185
negative_passages.text: Simplest way to integrate $\int \frac{1}{1+\tan x}dx,$