query: How to evaluate $\int_0^{\frac{\pi}{2}}\frac{dx}{1+\tan^{2013}x}$
positive_passages.docid: 2411
positive_passages.text: Integrate $\int_0^{\pi/2} \frac{1}{1+\tan^\alpha{x}}\,\mathrm{d}x$
negative_passages.docid: 143734
negative_passages.text: Evaluating $\int \frac{\sin\left(x\right)}{1+x^2}dx$
negative_passages.docid: 120168
negative_passages.text: How to calculate $\int_{0}^{\pi/2}{\{\tan(x)\}dx}$
negative_passages.docid: 149341
negative_passages.text: Help me evaluate $\int_0^1 \frac{\log(x+1)}{1+x^2} dx$
negative_passages.docid: 129892
negative_passages.text: show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
negative_passages.docid: 115759
negative_passages.text: Evaluating this integral : $ \int \frac {1-7\cos^2x} {\sin^7x \cos^2x} dx $
negative_passages.docid: 9653
negative_passages.text: Evaluate the integral $\int^{\frac{\pi}{2}}_0 \frac{\sin^3x}{\sin^3x+\cos^3x}\,\mathrm dx$.
negative_passages.docid: 11499
negative_passages.text: How to show the inequality for $\int_{0}^{\pi/4}\tan^n(x) dx$
negative_passages.docid: 142673
negative_passages.text: Evaluate $\tan^{2}(20^{\circ}) + \tan^{2}(40^{\circ}) + \tan^{2}(80^{\circ})$
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: 65847
negative_passages.text: To evaluate $\int_{0}^\pi \frac {\sin^2 x}{a^2-2ab \cos x + b^2}\mathrm dx$?
negative_passages.docid: 35861
negative_passages.text: Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
negative_passages.docid: 81057
negative_passages.text: Evaluation of $\int_{\frac{1}{e}}^{\tan x}\frac{t}{1+t^2}dt+\int_{\frac{1}{e}}^{\cot x}\frac{1}{t(1+t^2)}dt$
negative_passages.docid: 146338
negative_passages.text: How to evaluate $\int\frac{1+x^4}{(1-x^4)^{3/2}}dx$?
negative_passages.docid: 130736
negative_passages.text: Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$
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: 17925
negative_passages.text: Vardi's Integral: $\int_{\pi/4}^{\pi/2} \ln (\ln(\tan x))dx $