query: Evaluate $\int_0^\frac{\pi}{2} \frac{\cos^{9999}(x)}{\cos^{9999}(x)+sin^{9999}(x)} dx$
positive_passages.docid: 20016
positive_passages.text: How to integrate $\int_0^{\pi/2}\frac{\sin^nx}{\sin^nx+\cos^nx}dx$?
negative_passages.docid: 27910
negative_passages.text: How to evaluate $\int_0^{2\pi} \frac{d\theta}{A+B\cos\theta}$?
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: 93759
negative_passages.text: Evaluate $\int_{0}^{\infty} \frac{e^{ax}-e^{bx}}{(1+e^{ax})(1+e^{bx})} dx$
negative_passages.docid: 89499
negative_passages.text: Evaluating the integral $\int_0^{\frac{\pi}{2}}\log\left(\frac{1+a\cos(x)}{1-a\cos(x)}\right)\frac{1}{\cos(x)}dx$
negative_passages.docid: 156485
negative_passages.text: How to evaluate $\int_{0}^{2\pi}e^{\cos \theta}\cos( \sin \theta) d\theta$?
negative_passages.docid: 95403
negative_passages.text: Evaluating $\int \frac{\sec^2 x}{(\sec x + \tan x )^{{9}/{2}}}\,\mathrm dx$
negative_passages.docid: 150843
negative_passages.text: Evaluation of $\int_0^{\pi/4} \sqrt{\tan x} \sqrt{1-\tan x}\,\,dx$
negative_passages.docid: 31964
negative_passages.text: Evaluating $\int_0^{\infty}\frac{\ln(x^2+1)}{x^2+1}dx$
negative_passages.docid: 3704
negative_passages.text: Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
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: 151563
negative_passages.text: Evaluate: $\int_{0}^{\pi}\frac{\cos 2017x}{5-4\cos x}dx$
negative_passages.docid: 87242
negative_passages.text: Ways to prove $ \int_0^\pi dx \frac{\sin^2(n x)}{\sin^2 x} = n\pi$
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: 141892
negative_passages.text: How to evaluate $\int_0^\infty \frac{1}{x^n+1} dx$
negative_passages.docid: 16800
negative_passages.text: Integrating $\int_0^{2\pi} \frac1{a\cos(t)+b\sin(t)+c}dt$ with $\sqrt{a^2+b^2}=1<c$
negative_passages.docid: 115598
negative_passages.text: Evaluating $\int_{0}^{1} dx\frac{\log(1+x)}{1 + x^2}$