query: Evaluating $\int_{0}^{2\pi } \frac{\sin^{2} (x) }{5+4\cos(x)}\,\mathrm dx$
positive_passages.docid: 71988
positive_passages.text: Evaluate $\int_0^{2\pi} \frac{\sin^2\theta}{5+4\cos\theta}\,\mathrm d\theta$
negative_passages.docid: 136385
negative_passages.text: Integrate $ \int_{0}^{\frac{\pi}{4}}\tan^{-1}\left(\frac{\sqrt{2}\cos3 \phi}{\left(2\cos 2 \phi+ 3\right)\sqrt{\cos 2 \phi}}\right)d\phi$
negative_passages.docid: 139297
negative_passages.text: Find the sign of $\int_{0}^{2 \pi}\frac{\sin x}{x} dx$
negative_passages.docid: 27195
negative_passages.text: Evaluating $\int_{0}^{1}\frac{1-x}{1+x}\frac{\mathrm dx}{\ln x}$
negative_passages.docid: 130058
negative_passages.text: Evaluate $\int_0^{\pi} e^{a\cos(t)}\cos(a\sin t)dt$
negative_passages.docid: 144811
negative_passages.text: Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
negative_passages.docid: 123767
negative_passages.text: How to integrate $\int \frac{1}{\cos(x)}\,\mathrm dx$
negative_passages.docid: 129913
negative_passages.text: Evaluate: $I=\int\limits_{0}^{\frac{\pi}{2}}\ln\frac{(1+\sin x)^{1+\cos x}}{1+\cos x}dx$
negative_passages.docid: 63016
negative_passages.text: Integration of $\int\frac{1}{x^{4}+1}\mathrm dx$
negative_passages.docid: 95403
negative_passages.text: Evaluating $\int \frac{\sec^2 x}{(\sec x + \tan x )^{{9}/{2}}}\,\mathrm dx$
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: 3704
negative_passages.text: Evaluating the integral $\int_0^\infty \frac{\sin x} x \,\mathrm dx = \frac \pi 2$?
negative_passages.docid: 27002
negative_passages.text: Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
negative_passages.docid: 142619
negative_passages.text: Evaluating the complex integral $\int_{|z|=2}^{}\frac{1}{z^2+1}dz$
negative_passages.docid: 115759
negative_passages.text: Evaluating this integral : $ \int \frac {1-7\cos^2x} {\sin^7x \cos^2x} dx $
negative_passages.docid: 60654
negative_passages.text: Integrate $\int_0^{2 \pi } \frac{1}{(a+b \cos^2 (x))^2} \, \mathrm{d}x$
negative_passages.docid: 122913
negative_passages.text: Evaluate $\int \frac{\sec^{2}{x}}{(\sec{x} + \tan{x})^{5/2}} \ \mathrm dx$