query: $\int_0^{\pi/2}\frac{1}{1+\tan^{n}x}dx$
positive_passages.docid: 9653
positive_passages.text: Evaluate the integral $\int^{\frac{\pi}{2}}_0 \frac{\sin^3x}{\sin^3x+\cos^3x}\,\mathrm dx$.
negative_passages.docid: 92176
negative_passages.text: Solving $\lim_{n\to\infty}(n\int_0^{\pi/4}(\tan x)^ndx)$?
negative_passages.docid: 27002
negative_passages.text: Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
negative_passages.docid: 102932
negative_passages.text: Integral $\int_0^\infty \frac{\arctan(x) dx}{x(1+x^2)}$?
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: 123500
negative_passages.text: Integration of $\frac {1}{1+\sin x}$
negative_passages.docid: 101030
negative_passages.text: Integration $I_n=\int _0^{\pi }\sin^{2n}\theta d\theta $
negative_passages.docid: 17454
negative_passages.text: Evaluate the integral $\int_0^n \frac{f(x)}{f(x) + f(n-x)}dx $
negative_passages.docid: 57686
negative_passages.text: Finding $ \int^1_0 \frac{\ln(1+x)}{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: 20016
negative_passages.text: How to integrate $\int_0^{\pi/2}\frac{\sin^nx}{\sin^nx+\cos^nx}dx$?
negative_passages.docid: 4971
negative_passages.text: $\int_{0}^{1}\frac{1-x}{1+x}.\frac{dx}{\sqrt{x+x^2+x^3}}$
negative_passages.docid: 95403
negative_passages.text: Evaluating $\int \frac{\sec^2 x}{(\sec x + \tan x )^{{9}/{2}}}\,\mathrm dx$
negative_passages.docid: 117587
negative_passages.text: $\int_{0}^{1}\frac{\sin^{-1}\sqrt x}{x^2-x+1}dx$
negative_passages.docid: 6717
negative_passages.text: Evaluation of $\int_{\frac{1}{2014}}^{2014} \frac{\tan^{-1}x}{x} dx$
negative_passages.docid: 39629
negative_passages.text: Indefinite integration of $\int \frac{1}{1+\sqrt{x^2+2x+2}}dx$