query: Evaluate $\int_{0}^{\frac{\pi}{2}} \frac{\sin^2 nx}{\sin^2 x}\text{d}x$
positive_passages.docid: 29322
positive_passages.text: Evaluate $\int_{0}^{\frac{\pi}{2}} \frac{\sin^2 nx}{\sin x} \text{d}x$
negative_passages.docid: 65847
negative_passages.text: To evaluate $\int_{0}^\pi \frac {\sin^2 x}{a^2-2ab \cos x + b^2}\mathrm dx$?
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: 1416
negative_passages.text: closed form of $\int_{0}^{2\pi}\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^n}$
negative_passages.docid: 93174
negative_passages.text: Evaluate integral $\int_0^\pi \sin^4\left(x+\sin 3x\right)dx$
negative_passages.docid: 60491
negative_passages.text: Evaluate $ \int_{25\pi/4}^{53\pi/4}\frac{1}{(1+2^{\sin x})(1+2^{\cos x})}dx $
negative_passages.docid: 71982
negative_passages.text: Evaluating this integral $ \small\int \frac {x^2 dx} {(x\sin x+\cos x)^2} $
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: 130736
negative_passages.text: Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$
negative_passages.docid: 100401
negative_passages.text: Evaluate $\int \frac{1}{(x^2+1)^2}dx$
negative_passages.docid: 17679
negative_passages.text: Evaluate the integral $\int_0^{2a}\int_0^\sqrt{2ax-x^2}\frac{\phi'(y)(x^2+y^2)x dxdy}{\sqrt{4a^2x^2-(x^2+y^2)^2}}$
negative_passages.docid: 119669
negative_passages.text: Evaluate $\int \frac{1}{\sin x\cos x} dx $
negative_passages.docid: 54638
negative_passages.text: Integral $\int^{ \pi /2}_{0} \ln (\sin x)\ dx$
negative_passages.docid: 29425
negative_passages.text: $\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \mathrm {d}x$ Evaluate Integral
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: 137060
negative_passages.text: Evaluating $\int_0^{\tfrac{\pi}{4}}\ln(\cos x-\sin x)\ln(\cos x) dx - \int_0^{\tfrac{\pi}{4}}\ln(\cos x+\sin x)\ln(\sin x)dx=\frac{G\ln 2}{2}$
negative_passages.docid: 95933
negative_passages.text: How to evaluate the integral $\int_0^{\pi}\frac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx$?