query: To calculate the integral $\int_{0}^\pi e^{k \cos \theta} \cos(k \sin \theta)d\theta$
positive_passages.docid: 153318
positive_passages.text: Calculating the following integral using complex analysis: $\int_{0}^{\pi}e^{a\cos(\theta)}\cos(a\sin(\theta))\, d\theta$
negative_passages.docid: 79044
negative_passages.text: Using the residue theorem, calculate $\int_{0}^{2\pi}\frac{1}{1-2a\cos{\theta}+a^2}d\theta$
negative_passages.docid: 29602
negative_passages.text: Integral $ \int_{-\pi/2}^{\pi/2} \frac{1}{2007^x+1}\cdot \frac{\sin^{2008}x}{\sin^{2008}x+\cos^{2008}x}dx $
negative_passages.docid: 139297
negative_passages.text: Find the sign of $\int_{0}^{2 \pi}\frac{\sin x}{x} dx$
negative_passages.docid: 155422
negative_passages.text: Evaluating $\int_{0}^{\frac{\pi}{2}}\frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}}\, \mathrm{d}x$
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: 39697
negative_passages.text: Integration of $e^{ax}\cos bx$ and $e^{ax}\sin bx$
negative_passages.docid: 86857
negative_passages.text: Integrate $\int_{0}^{2\pi}\log|1-e^{i\theta}| d\theta$
negative_passages.docid: 105619
negative_passages.text: Finding $\int_{0}^{\pi/2} \frac{\tan x}{1+m^2\tan^2{x}} \mathrm{d}x$
negative_passages.docid: 121071
negative_passages.text: Calculation of $\int^{\pi/2}_{0}\cos^{n}(x)\cos (nx)\,dx$, where $n\in \mathbb{N}$
negative_passages.docid: 112868
negative_passages.text: calculate an integration by using residue theorem
negative_passages.docid: 128600
negative_passages.text: How to evaluate this integral$\int_{-\infty}^\infty\dfrac{\omega^\alpha e^{i\omega t}}{(\omega_0^2-\omega^2)^{2}+4(\zeta\omega_0\omega)^2}\,d\omega$
negative_passages.docid: 101030
negative_passages.text: Integration $I_n=\int _0^{\pi }\sin^{2n}\theta d\theta $
negative_passages.docid: 518
negative_passages.text: What is the integral of $\int e^x\,\sin x\,\,dx$?
negative_passages.docid: 51991
negative_passages.text: What is the integral of $e^{\cos x}$
negative_passages.docid: 98741
negative_passages.text: Finding $\int_{0}^{\frac{\pi}{4}} \frac{\tan \theta - \tan^3 \theta}{\ln \tan \theta}$
negative_passages.docid: 79633
negative_passages.text: Calculating the integral $\int_{-\infty}^{\infty} x\sin(x)/(x^2+1)^2 dx$