query: $\int^{\pi/2}_{0}\frac{\theta \cos(\theta)}{1+\sin^{2}(\theta)}$ through complex analysis
positive_passages.docid: 18672
positive_passages.text: Integrate $\int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$
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: 91196
negative_passages.text: Complex Integration of $\int_0^\infty e^{-ax}\cos(bx)\,dx$
negative_passages.docid: 151063
negative_passages.text: Calculate $\int_{0}^{\frac{\pi}{2}}\frac{\sin^{3}(t)}{\sin^{3}(t)+\cos^{3}(t)}dt$ by hands
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: 153867
negative_passages.text: Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
negative_passages.docid: 62109
negative_passages.text: $\int_{-\infty}^{\infty} \frac{\cos(αx)}{(x^2+1)(x^2+4)} \mathrm dx$ using Complex methods
negative_passages.docid: 21240
negative_passages.text: Prove $\int_0^{\infty}\! \frac{\mathbb{d}x}{1+x^n}=\frac{\pi}{n \sin\frac{\pi}{n}}$ using real analysis techniques only
negative_passages.docid: 20016
negative_passages.text: How to integrate $\int_0^{\pi/2}\frac{\sin^nx}{\sin^nx+\cos^nx}dx$?
negative_passages.docid: 100817
negative_passages.text: Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$
negative_passages.docid: 104512
negative_passages.text: Why is $\frac{1}{2\pi i}\int_{\gamma}\frac{f'(z)}{f(z)}dz$ an integer?
negative_passages.docid: 114734
negative_passages.text: Prove that $\frac{1}{2\pi i}\int_\mathcal{C} |1+z+z^2+\cdots+z^{2n}|^2~dz =2n$ where $\mathcal{C}$ is the unit circle
negative_passages.docid: 104904
negative_passages.text: Calculating $\int_0^\infty \frac {\sin^2x}{x^2}dx$ using the Residue Theorem.
negative_passages.docid: 100711
negative_passages.text: $\int_{-\infty}^{\infty}e^{-zt^2 + 2wt} \ dt = e^{w^2 / z} \sqrt{\frac{\pi}{z}}$ for $z,w \in \mathbb{C}, Re(z) > 0$
negative_passages.docid: 118701
negative_passages.text: Evaluate $\int_{0}^{\frac{\pi }{2}}\frac{x dx}{\sin x +\cos x}$
negative_passages.docid: 152336
negative_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: 145183
negative_passages.text: finding $\int_0^\infty \dfrac{dx}{1+x^4}$ through complex analysis