Is is true that $\int_0^1\sin(\pi x)\,x^x\,(1-x)^{1-x}\,dx\ =\ \frac1{4!}e\pi$?
28771
Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $
80710
Does $\int_{-1}^1 \frac 1 x dx$ equal zero?
130058
Evaluate $\int_0^{\pi} e^{a\cos(t)}\cos(a\sin t)dt$
50509
Prove that $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}}~dx=0$ (without trigonometric substitution)
130736
Integrating $\int^0_\pi \frac{x \sin x}{1+\cos^2 x}$
70715
How do I prove $\int_0^\pi\frac{(\sin nx)^2}{(\sin x)^2}dx = n\pi$?
74241
Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
99753
How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?
132124
$\int_{0}^{\infty}\frac{x}{x^3+1}dx$ =?
150843
Evaluation of $\int_0^{\pi/4} \sqrt{\tan x} \sqrt{1-\tan x}\,\,dx$
68241
Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
25797
Integral of $ x \ln( \sin (x))$ from 0 to $ \pi $
119669
Evaluate $\int \frac{1}{\sin x\cos x} dx $
77053
Evaluating $\int_{0}^{1}\frac{\arcsin{\sqrt{x}}}{x^4-2x^3+2x^2-x+1}\operatorname d\!x$
63016
Integration of $\int\frac{1}{x^{4}+1}\mathrm dx$
31660
Integral $\int_{0}^{1}\left\{\frac{1}{x}\right\}\left\{\frac{1}{1-x}\right\}\left\{1-\frac{1}{x}\right\} d x=?$
36366
Prove $\int_0^\infty \frac{\sin^4x}{x^4}dx = \frac{\pi}{3}$