How to use complex analysis to evaluate the trigonometric integral $\int_{0}^{2 \pi}{\frac {\cos \left( x \right) }{2+\cos \left( x \right) }}$
96414
Using residues to evaluate the integral $\int_{-\pi}^{\pi} \frac{\cos(n\theta)}{1-2a\cos(\theta)+a^2}d\theta$, $|a|<1$
44059
Evaluating $\int_{-1}^{1}\frac{\arctan{x}}{1+x}\ln{\left(\frac{1+x^2}{2}\right)}dx$
71988
Evaluate $\int_0^{2\pi} \frac{\sin^2\theta}{5+4\cos\theta}\,\mathrm d\theta$
60491
Evaluate $ \int_{25\pi/4}^{53\pi/4}\frac{1}{(1+2^{\sin x})(1+2^{\cos x})}dx $
27002
Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
151063
Calculate $\int_{0}^{\frac{\pi}{2}}\frac{\sin^{3}(t)}{\sin^{3}(t)+\cos^{3}(t)}dt$ by hands
130058
Evaluate $\int_0^{\pi} e^{a\cos(t)}\cos(a\sin t)dt$
143734
Evaluating $\int \frac{\sin\left(x\right)}{1+x^2}dx$
63167
Evaluate integral $\int_0^\frac{\pi}{2} \ln\left(\frac{1+a\cos x}{1-a\cos x}\right) \frac{\mathrm{d} x}{\cos x}$ for $\left|a\right|<1$
95933
How to evaluate the integral $\int_0^{\pi}\frac{a^n\sin^2x+b^n\cos^2x}{a^{2n}\sin^2x+b^{2n}\cos^2x}dx$?
130668
Evaluating the integral with trigonometric integrand
10341
complex integration $\frac{1-|a|^{2}}{\pi}\int_{L}\frac{|dz|}{{|z+a|}^{2}}$
80553
Show that,$\int_0^\pi \left|\frac{\sin nx}{x}\right|\mathrm{d}x \ge \frac{2}{\pi}\left(1+\frac12+\cdots+\frac{1}{n}\right)$
29370
Trig integral $\int ( \cos{x} + \sin{x}\cos{x}) \, dx $
63650
Evaluating the contour integral $\int_{0}^{\infty}\frac{\sin^{3}(x)}{x^{3}}\mathrm dx$
111775
$\int_{-\infty}^{+\infty} e^{-x^2} dx$ with complex analysis
18836
Complex integral over a circle