query: Getting incorrect answers when computing $\int_{0}^a \frac{\cos(\pi n x/a)}{x^2+a^2}\ \! \mathrm dx$?
positive_passages.docid: 142834
positive_passages.text: An integral : $\int_{-a}^a \frac{\cos(\pi n x/a)}{x^2+a^2}\mathrm dx$
negative_passages.docid: 89956
negative_passages.text: Is the integral $\int_0^\infty \frac{\mathrm{d} x}{(1+x^2)(1+x^a)}$ equal for all $a \neq 0$?
negative_passages.docid: 67326
negative_passages.text: How to solve $ \int \limits _0 ^{2\pi} \dfrac{dx}{(\alpha +\beta\cos x)^2} $
negative_passages.docid: 75423
negative_passages.text: Computing $\int_0^\infty\frac{1}{(1+x^{2015})(1+x^2)}$
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: 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: 150843
negative_passages.text: Evaluation of $\int_0^{\pi/4} \sqrt{\tan x} \sqrt{1-\tan x}\,\,dx$
negative_passages.docid: 38773
negative_passages.text: Suppose $ \alpha, \beta>0 $. Compute: $ \int_{0}^{\infty}\frac{\cos (\alpha x)-\cos (\beta x)}{x}dx $
negative_passages.docid: 123767
negative_passages.text: How to integrate $\int \frac{1}{\cos(x)}\,\mathrm dx$
negative_passages.docid: 70013
negative_passages.text: How to calculate $\int \frac{x^2 }{(x^2+1)^2} dx$?
negative_passages.docid: 102156
negative_passages.text: Integral of $\int_0^{\pi/2} \frac {\sqrt{\sin x}}{\sqrt {\sin x} + \sqrt {\cos x}}$dx
negative_passages.docid: 135447
negative_passages.text: Compute the integral $\int_0^{\frac\pi2}\frac{\mathrm d \theta}{\sqrt{\sin \theta}}$
negative_passages.docid: 106803
negative_passages.text: How to see $\cos x \leq \exp(-x^2/2)$ on $x \in [0,\pi/2]$?
negative_passages.docid: 70715
negative_passages.text: How do I prove $\int_0^\pi\frac{(\sin nx)^2}{(\sin x)^2}dx = n\pi$?
negative_passages.docid: 7835
negative_passages.text: Tricky elementary integral $\int_{0}^{\frac{\pi}{2}}x\cot(x)dx$.
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: 130736
negative_passages.text: Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$