Prove $\int_{0}^{1}{(x-1)^2\over \sqrt{2^x-1}\ln(2^x-1)}dx={\pi\over \ln^2{2}}$
78008
A conjectured closed form of $\int\limits_0^\infty\frac{x-1}{\sqrt{2^x-1}\ \ln\left(2^x-1\right)}dx$
79908
Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$
74241
Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
70715
How do I prove $\int_0^\pi\frac{(\sin nx)^2}{(\sin x)^2}dx = n\pi$?
28771
Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $
138174
Integral $\int_0^1 \frac{x\ln\left(\frac{1+x}{1-x}\right)}{\left(\pi^2+\ln^2\left(\frac{1+x}{1-x}\right)\right)^2}dx$
107774
Prove $\|x\|_1\le \sqrt n \|x\|_2$
47793
Integral $\int_0^1\sqrt{1-x^4}dx$
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
1626
How do we prove $\int_I\int_x^1\frac{1}{t}f(t)\text{ dt}\text{ dx}=\int_If(x)\text{ dx}$
45841
integral of $\int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx$ using contour integration?
6483
Computing $\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right) \, dx$
90313
Integrate $\int_0^\pi{{x\sin x}\over{1+\cos^2x}}dx$.
7903
Prove that $B[x] \cap B[x^{-1}]$ is integral over $B$
137060
Evaluating $\int_0^{\tfrac{\pi}{4}}\ln(\cos x-\sin x)\ln(\cos x) dx - \int_0^{\tfrac{\pi}{4}}\ln(\cos x+\sin x)\ln(\sin x)dx=\frac{G\ln 2}{2}$
90245
Computing $\int^1_0 \frac{p^2-1}{\text{ln } p}dp$
100869
How to show that $\int_0^1 \left(\sqrt[3]{1-x^7} - \sqrt[7]{1-x^3}\right)\;dx = 0$