query: Calculate integral $\int_{0}^{2\pi} \frac{dx}{a^2\sin^2x+b^2\cos^2x}$
positive_passages.docid: 152336
positive_passages.text: Any hint to solve given integral $\int_0^{2{\pi}}{{d\theta}\over{a^2\cos^2\theta+b^2\sin^2\theta}}$?
negative_passages.docid: 148613
negative_passages.text: Integrate $\int_{0}^{1}{x^{-x}(1-x)^{x-1}\sin{\pi x}dx}$
negative_passages.docid: 153867
negative_passages.text: Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\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: 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: 27002
negative_passages.text: Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
negative_passages.docid: 106544
negative_passages.text: Solve $ \frac{2}{\pi}\int_{-\pi}^\pi\frac{\sin\frac{9x}{2}}{\sin\frac{x}{2}}dx $
negative_passages.docid: 130736
negative_passages.text: Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$
negative_passages.docid: 110922
negative_passages.text: What are different ways to compute $\int_{0}^{+\infty}\frac{\cos x}{a^2+x^2}dx$?
negative_passages.docid: 30002
negative_passages.text: Calculate the integral $\int_{0}^{2\pi}\frac{1}{a^{2}\cos^2t+b^{2}\sin^{2}t}dt$, by deformation theorem.
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: 60654
negative_passages.text: Integrate $\int_0^{2 \pi } \frac{1}{(a+b \cos^2 (x))^2} \, \mathrm{d}x$
negative_passages.docid: 55738
negative_passages.text: Evaluating $\int _0^{\frac{\pi }{2}}\:\frac{\sqrt[3]{\sin^2\left(x\right)}}{\sqrt[3]{\sin^2\left(x\right)}+\sqrt[3]{\cos^2\left(x\right)}}dx$
negative_passages.docid: 8642
negative_passages.text: Calculate $ \int_{-2}^{0} \frac{x}{\sqrt{e^x+(x+2)^2}} dx $
negative_passages.docid: 65093
negative_passages.text: Integrate $\int \sin^4x \cos^2x dx$
negative_passages.docid: 130668
negative_passages.text: Evaluating the integral with trigonometric integrand
negative_passages.docid: 126576
negative_passages.text: Most efficient way to integrate $\int_0^\pi \sqrt{4\sin^2 x - 4\sin x + 1}\,dx$?