query: Evaluate the integral $\int_0^{2\pi} \frac {dx}{1-2r\cos(x)+r^2}$ and $0<r<1$
positive_passages.docid: 153283
positive_passages.text: Trigonometric Integral Using Residue Theorem
negative_passages.docid: 55738
negative_passages.text: Evaluating $\int _0^{\frac{\pi }{2}}\:\frac{\sqrt[3]{\sin^2\left(x\right)}}{\sqrt[3]{\sin^2\left(x\right)}+\sqrt[3]{\cos^2\left(x\right)}}dx$
negative_passages.docid: 144811
negative_passages.text: Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
negative_passages.docid: 60654
negative_passages.text: Integrate $\int_0^{2 \pi } \frac{1}{(a+b \cos^2 (x))^2} \, \mathrm{d}x$
negative_passages.docid: 29602
negative_passages.text: Integral $ \int_{-\pi/2}^{\pi/2} \frac{1}{2007^x+1}\cdot \frac{\sin^{2008}x}{\sin^{2008}x+\cos^{2008}x}dx $
negative_passages.docid: 60491
negative_passages.text: Evaluate $ \int_{25\pi/4}^{53\pi/4}\frac{1}{(1+2^{\sin x})(1+2^{\cos x})}dx $
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: 84826
negative_passages.text: Evaluating $\int_0^{2 \pi} e^{\cos x} \cos (nx - \sin x) \,dx$ using complex analysis
negative_passages.docid: 6483
negative_passages.text: Computing $\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right) \, dx$
negative_passages.docid: 60944
negative_passages.text: Evaluating an integral with ${\mathrm{d}t}$ in the numerator, $\int \frac{\mathrm{d}t}{\cos(t)^2}$.
negative_passages.docid: 97582
negative_passages.text: How do I evaluate this integral $\int_0^\pi{\frac{{{x^2}}}{{\sqrt 5-2\cos x}}}\operatorname d\!x$?
negative_passages.docid: 31964
negative_passages.text: Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$
negative_passages.docid: 16712
negative_passages.text: Evaluate $\int_{-\pi/4}^{\pi/4}(\cos(t)+\sqrt{1+t^2}\cos(t)^3\sin (t)^3)dt$
negative_passages.docid: 84765
negative_passages.text: Evaluating $\int_{-\infty}^{\infty}\frac{1}{(x^2+b^2)^2}dx$
negative_passages.docid: 81621
negative_passages.text: How to evaluate the integral $\int_{0}^{\infty}\frac{\cos {(ax)}-\cos{(b x)}}{x^2 }dx$?
negative_passages.docid: 150843
negative_passages.text: Evaluation of $\int_0^{\pi/4} \sqrt{\tan x} \sqrt{1-\tan x}\,\,dx$
negative_passages.docid: 9653
negative_passages.text: Evaluate the integral $\int^{\frac{\pi}{2}}_0 \frac{\sin^3x}{\sin^3x+\cos^3x}\,\mathrm dx$.