Prove $\int ^{\pi/2}_0 \frac{\sin^m x}{\sin^m x+\cos^m x}dx=\frac{\pi}{4}$
9653
Evaluate the integral $\int^{\frac{\pi}{2}}_0 \frac{\sin^3x}{\sin^3x+\cos^3x}\,\mathrm dx$.
64480
How do I find $\int_{0}^{\infty} \frac{\sin^4 x}{x^2}\,dx$?
83703
Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $
139057
Showing that $\frac{1}{2\pi}\int^{2\pi}_{0}(2\cos\theta)^{2n}d\theta=\frac{(2n)!}{n!n!}$
41191
How to prove this $\pi$ formula?
127759
Prove that $\frac{\sin(a)}{\sin(b)} < \frac{a}{b} < \frac{\tan(a)}{\tan(b)}$ where $0 < b < a < \frac{\pi}{2}$
158279
$\int_0^{\pi/2}\ln(\sin(x))$?
105619
Finding $\int_{0}^{\pi/2} \frac{\tan x}{1+m^2\tan^2{x}} \mathrm{d}x$
88154
Proving $\int_{0}^1\frac{x-1}{\log x}dx=\log 2$ and $\int_{0}^1\frac{\log x}{x-1}dx=\frac{\pi^2}{6}$
99584
Evaluation of $\int \frac{\sqrt{\sin ^4x+\cos ^4x}}{\sin ^3x \cos x }dx$
130736
Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$
24311
Proving $\frac{\sin x}{x} =\left(1-\frac{x^2}{\pi^2}\right)\left(1-\frac{x^2}{2^2\pi^2}\right) \left(1-\frac{x^2}{3^2\pi^2}\right)\cdots$
48586
Prove: $\cot x=\sin x\,\sin\left(\frac{\pi}{2}-x\right)+\cos^2x\,\cot x$
26096
Evaluating $\int \frac{\sin{x}+\cos{x}}{\sin^4{x}+\cos^4{x}} \mathrm dx$
50509
Prove that $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}}~dx=0$ (without trigonometric substitution)
114734
Prove that $\frac{1}{2\pi i}\int_\mathcal{C} |1+z+z^2+\cdots+z^{2n}|^2~dz =2n$ where $\mathcal{C}$ is the unit circle
117587
$\int_{0}^{1}\frac{\sin^{-1}\sqrt x}{x^2-x+1}dx$