Evaluate $\int_0^{\frac{\pi}{4}}\arctan\frac{\sqrt{2}\cos 3x}{(3+2\cos 2x)\sqrt{\cos 2x}}{\rm d}x$.
136385
Integrate $ \int_{0}^{\frac{\pi}{4}}\tan^{-1}\left(\frac{\sqrt{2}\cos3 \phi}{\left(2\cos 2 \phi+ 3\right)\sqrt{\cos 2 \phi}}\right)d\phi$
147479
Evaluate $\int \frac{2-3x}{2+3x}\sqrt\frac{1+x}{1-x}dx$
36701
$\displaystyle\int_{0}^{2\pi}\frac{1}{a+ \cos\theta}\,d\theta$
147641
How to evaluate $\int \frac { \sin x+\cos x }{ \sin^4 x+\cos^4x}\, dx$?
151563
Evaluate: $\int_{0}^{\pi}\frac{\cos 2017x}{5-4\cos x}dx$
153867
Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
93174
Evaluate integral $\int_0^\pi \sin^4\left(x+\sin 3x\right)dx$
149866
Evaluating $\int_0^{2\pi} \frac {\cos(\theta)}{5-3\cos(\theta)} \, d\theta$ using residue theorem
31716
Calculate :$\int_{0}^{2\pi }e^{R{ {\cos t}}}\cos(R\sin t+3t)\mathrm{d}t$
41416
Integrating $ \int_2^4 \frac{ \sqrt{\ln(9-x)} }{ \sqrt{\ln(9-x)}+\sqrt{\ln(x+3)} } dx. $
17679
Evaluate the integral $\int_0^{2a}\int_0^\sqrt{2ax-x^2}\frac{\phi'(y)(x^2+y^2)x dxdy}{\sqrt{4a^2x^2-(x^2+y^2)^2}}$
46706
Integral $\int_0^2 \frac{\arctan x}{x^2+2x+2}dx$
129913
Evaluate: $I=\int\limits_{0}^{\frac{\pi}{2}}\ln\frac{(1+\sin x)^{1+\cos x}}{1+\cos x}dx$
150843
Evaluation of $\int_0^{\pi/4} \sqrt{\tan x} \sqrt{1-\tan x}\,\,dx$
156485
How to evaluate $\int_{0}^{2\pi}e^{\cos \theta}\cos( \sin \theta) d\theta$?
96414
Using residues to evaluate the integral $\int_{-\pi}^{\pi} \frac{\cos(n\theta)}{1-2a\cos(\theta)+a^2}d\theta$, $|a|<1$
36128
Using differentiation for computing $\int_{0}^{1}\frac{\arctan(ax)}{x\sqrt{1-x^2}}\,dx$