query: Compute the real integral $ \int\limits_0^{2\pi} \frac{d \theta}{2+\sin{\theta}}$ by writing the sine function in terms of the exponential function
positive_passages.docid: 144811
positive_passages.text: Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
negative_passages.docid: 156485
negative_passages.text: How to evaluate $\int_{0}^{2\pi}e^{\cos \theta}\cos( \sin \theta) d\theta$?
negative_passages.docid: 156531
negative_passages.text: Evaluating the integral $\int_{-\infty}^\infty \frac{\sin^2(x)}{x^2}e^{i t x} dx$
negative_passages.docid: 123899
negative_passages.text: $\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$
negative_passages.docid: 158971
negative_passages.text: Computing the Fourier series of $f(\theta)=(\pi-\theta)^2/4$ for $0\leq\theta\leq{2\pi}$
negative_passages.docid: 95637
negative_passages.text: Justifying Calculations on $f(n)=\frac{1}{2 \pi}\int_{-\pi}^{\pi}\theta e^{-in \theta} d \theta$
negative_passages.docid: 86857
negative_passages.text: Integrate $\int_{0}^{2\pi}\log|1-e^{i\theta}| d\theta$
negative_passages.docid: 29425
negative_passages.text: $\int_{0}^{\infty}\frac{\sin^{2n+1}(x)}{x} \mathrm {d}x$ Evaluate Integral
negative_passages.docid: 104138
negative_passages.text: How to integrate $\int\limits_0^\infty e^{-a x^2}\cos(b x) dx$ where $a>0$
negative_passages.docid: 34967
negative_passages.text: Compute $ \int_{0}^{ \infty }\frac{\ln xdx}{x^{2}+ax+b}$
negative_passages.docid: 129734
negative_passages.text: Computing $\sum_{k=1}^{\infty}\frac{1}{k}\int_{\pi k}^{\infty}\frac{\sin(x)}{x}dx$
negative_passages.docid: 65337
negative_passages.text: Compute $\int_{0}^{\infty}\frac{x\sin 2x}{9+x^{2}} \, dx$
negative_passages.docid: 75423
negative_passages.text: Computing $\int_0^\infty\frac{1}{(1+x^{2015})(1+x^2)}$
negative_passages.docid: 27910
negative_passages.text: How to evaluate $\int_0^{2\pi} \frac{d\theta}{A+B\cos\theta}$?
negative_passages.docid: 21088
negative_passages.text: Prove $\int\limits_{0}^{\pi/2}\frac{dx}{1+\sin^2{(\tan{x})}}=\frac{\pi}{2\sqrt{2}}\bigl(\frac{e^2+3-2\sqrt{2}}{e^2-3+2\sqrt{2}}\bigr)$
negative_passages.docid: 18672
negative_passages.text: Integrate $\int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$
negative_passages.docid: 65407
negative_passages.text: Evaluating $\int\limits_0^\infty \frac{\log x} {(1+x^2)^2} dx$ with residue theory