query: Solving the integral $\int_0^{\frac\pi2}\frac{dx}{1+\sin^2(\tan x)}$
positive_passages.docid: 21088
positive_passages.text: Prove $\int\limits_{0}^{\pi/2}\frac{dx}{1+\sin^2{(\tan{x})}}=\frac{\pi}{2\sqrt{2}}\bigl(\frac{e^2+3-2\sqrt{2}}{e^2-3+2\sqrt{2}}\bigr)$
negative_passages.docid: 81337
negative_passages.text: How to solve $(1-\tan^2x)\sec^2x+2^{\tan^2x}=0$
negative_passages.docid: 29322
negative_passages.text: Evaluate $\int_{0}^{\frac{\pi}{2}} \frac{\sin^2 nx}{\sin x} \text{d}x$
negative_passages.docid: 46706
negative_passages.text: Integral $\int_0^2 \frac{\arctan x}{x^2+2x+2}dx$
negative_passages.docid: 155422
negative_passages.text: Evaluating $\int_{0}^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}\, \mathrm{d}x$
negative_passages.docid: 98741
negative_passages.text: Finding $\int_{0}^{\frac{\pi}{4}} \frac{\tan \theta - \tan^3 \theta}{\ln \tan \theta}$
negative_passages.docid: 126054
negative_passages.text: calculate $\int_o^\pi \frac{x\sin x}{1+\cos^2x} \,dx$
negative_passages.docid: 119410
negative_passages.text: Solution of $\int_0^\infty\frac{\ln(1+{x^2})}{1+{x^2}}$
negative_passages.docid: 98787
negative_passages.text: Calculation of $\int \sqrt{\tan x+2}dx$
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: 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: 127284
negative_passages.text: Closed form of $\int_0^{\pi/2} \frac{\arctan^2 (\sin^2 \theta)}{\sin^2 \theta}\,d\theta$
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 $\int^{\frac{\pi}{2}}_0 \frac{\sin^3x}{\sin^3x+\cos^3x}\,\mathrm dx$.
negative_passages.docid: 137551
negative_passages.text: integral $\int_0^\pi \frac{\cos(2t)}{a^2\sin^2(t)+b^2\cos^2(t)}dt$
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: 129892
negative_passages.text: show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$