The function $f(x)=\int_0^{2\pi}\ln\left(x^2-2x\cos t+1\right)\,dt$
6483
Computing $\int_{0}^{\pi}\ln\left(1-2a\cos x+a^2\right) \, dx$
20021
Convolution integral $\int_0^t \cos(t-s)\sin(s)\ ds$
140386
Integrate $\int {\dfrac{x^2+\left(n-1\right)n}{\left(x\sin x+n\cos x\right)^2}}dx $
48881
Verification the integral identity $\int_0^\pi \ln(1+\alpha\cos(x))dx=\pi\ln\left(\frac{1+\sqrt{1-\alpha^2}}{2}\right)$.
64800
Evaluate $\int_0^1 \log \left( \frac{x^2+\sqrt{3}x+1}{x^2-\sqrt{3}x+1} \right) \frac{dx}{x} $
26444
How can I integrate $\ln \left( x+\sqrt{1+x^2} \right) $?
93610
What is $\int_0^1 \frac{\log \left(1-x^2\right) \sin ^{-1}(x)^2}{x^2} \, dx$?
30829
A question in Complex Analysis $\int_0^{2\pi}\log(1-2r\cos x +r^2)\,dx$
150809
Compute $ \int_0^1\frac{\ln^2(1+x)}{1+x^2}\, dx$
23522
Exponential integral $ \int_0^\infty \frac{x^t}{\Gamma(t+1)}\text dt$
5034
A closed form of $\int_0^1\frac{\ln\ln\left({1}/{x}\right)}{x^2-x+1}\mathrm dx$
154612
$\int_{0}^{x} f(t) dt \ge {f(x)}$ holds or not on $[0,1]$
17996
Integral $\int_0^1 \frac{\ln(x+\sqrt{1-x^2})}{x}dx$
66852
Integral $ \int_{-\infty}^{\infty}\frac{x^{2}}{\cosh\left(x\right)}\,{\rm d}x $
51837
Show that $\int_{0}^{\pi} xf(\sin(x))\text{d}x = \frac{\pi}{2}\int_{0}^{\pi}f(\sin(x))\text{d}x$
137060
Evaluating $\int_0^{\tfrac{\pi}{4}}\ln(\cos x-\sin x)\ln(\cos x) dx - \int_0^{\tfrac{\pi}{4}}\ln(\cos x+\sin x)\ln(\sin x)dx=\frac{G\ln 2}{2}$
142516
Evaluating the integral, $\int_{0}^{\infty} \ln\left(1 - e^{-x}\right) \,\mathrm dx $