Using the Argument Principle, evaluate $\int_{|z|=4}\frac{2z\sin(z)+z^2\cos(z)}{z^2\sin(z)}dz$.
127129
Using the Argument Principle, evaluate $\int_{|z-i|=7}\frac{z\sinh(z)+3\cosh(z)z}{z\cosh(z)}dz$.
118701
Evaluate $\int_{0}^{\frac{\pi }{2}}\frac{x dx}{\sin x +\cos x}$
16820
Evaluate $\int_{\gamma} \frac{ |dz| }{z} $ where $\gamma $ is the unit circle
71982
Evaluating this integral $ \small\int \frac {x^2 dx} {(x\sin x+\cos x)^2} $
153867
Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
18672
Integrate $\int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$
61466
what is $\int_{|z|=3}\frac{1}{(z-2)^n(z-4)^m}dz$ for $m,n\in\mathbb{N}$?
10070
Complex analysis: Calculating $\int_{-\infty}^{\infty} \frac{\sin x}{x} dx$ by using $f(z) = \frac{e^{iz} - 1}{iz}$
130058
Evaluate $\int_0^{\pi} e^{a\cos(t)}\cos(a\sin t)dt$
129892
show $\int_0^{\infty} \frac{x\sin ax}{x^2+t^2}dx = \frac{\pi}{2}e^{-at}$
143734
Evaluating $\int \frac{\sin\left(x\right)}{1+x^2}dx$
148746
Calculating $\int\frac{e^{iz}}{z}\, dz$ on the semi-circle given by $re^{i\theta}$ where $\theta:\,0\to\pi$
27002
Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
53519
Finding $\int_0^1{\frac{x^4(1-x)^4}{1+x^2}}dx$
129675
How to integrate $\int \frac{1}{\sin^4x + \cos^4 x} \,dx$?
38511
Evaluation of $\int\frac{1}{x^2.(x^4+1)^{\frac{3}{4}}}dx$
58909
Evaluation of $\int\frac{dx}{x+ \sqrt{x^2-x+1}}$