query: Calculation of $\int_0^{\pi/2} \frac{dx}{(1+x^2)(1+\tan x)}$
positive_passages.docid: 153867
positive_passages.text: Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
negative_passages.docid: 79044
negative_passages.text: Using the residue theorem, calculate $\int_{0}^{2\pi}\frac{1}{1-2a\cos{\theta}+a^2}d\theta$
negative_passages.docid: 67608
negative_passages.text: Integration of $1/(x^2+x\sqrt{x})$
negative_passages.docid: 124401
negative_passages.text: How to evaluate $\int_0^{2\pi}\frac{1}{(1+a\cos {\theta})^2}\,d\theta$ without contour integration?
negative_passages.docid: 143734
negative_passages.text: Evaluating $\int \frac{\sin\left(x\right)}{1+x^2}dx$
negative_passages.docid: 39629
negative_passages.text: Indefinite integration of $\int \frac{1}{1+\sqrt{x^2+2x+2}}dx$
negative_passages.docid: 45872
negative_passages.text: Integration: $\int\frac{1}{(x^2+x+1)^{1/2}} dx$
negative_passages.docid: 121071
negative_passages.text: Calculation of $\int^{\pi/2}_{0}\cos^{n}(x)\cos (nx)\,dx$, where $n\in \mathbb{N}$
negative_passages.docid: 71611
negative_passages.text: Evaluating $\int\sqrt{\frac{1-x^2}{1+x^2}}\mathrm dx$
negative_passages.docid: 62450
negative_passages.text: Computing $ \int_0^{2\pi} \frac{1}{a^2\cos^2 t+b^2 \sin^2 t} dt \;; a,b>0$.
negative_passages.docid: 118800
negative_passages.text: Calculating $\int_0^\pi \log(1-2a\cos (x)+a^2)\,dx$
negative_passages.docid: 53519
negative_passages.text: Finding $\int_0^1{\frac{x^4(1-x)^4}{1+x^2}}dx$
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: 24022
negative_passages.text: Compute $\int _0 ^{2\pi} (\sum_{n=1}^\infty \frac {\cos(nx)}{2^n})^2 dx$
negative_passages.docid: 123500
negative_passages.text: Integration of $\frac {1}{1+\sin x}$
negative_passages.docid: 2411
negative_passages.text: Integrate $\int_0^{\pi/2} \frac{1}{1+\tan^\alpha{x}}\,\mathrm{d}x$
negative_passages.docid: 137060
negative_passages.text: Evaluating $\int_0^{\tfrac{\pi}{4}}\ln(\cos x-\sin x)\ln(\cos x) dx - \int_0^{\tfrac{\pi}{4}}\ln(\cos x+\sin x)\ln(\sin x)dx=\frac{G\ln 2}{2}$