Integral $\int_0^{\infty}\frac{\ln(x)}{x^2+nx+n^2}dx=\frac{2\pi}{3\sqrt{3}}\frac{\ln(n)}{n}$
34967
Compute $ \int_{0}^{ \infty }\frac{\ln xdx}{x^{2}+ax+b}$
19514
$\int_0^{\infty } \frac{\log (x)}{e^x+1} \, dx = -\frac{1}{2} \log ^2(2)$ How to show?
148743
$\int_0^\infty \frac{1}{1+x^ 9} \, dx$
102932
Integral $\int_0^\infty \frac{\arctan(x) dx}{x(1+x^2)}$?
25797
Integral of $ x \ln( \sin (x))$ from 0 to $ \pi $
121736
An improper integral : $\int_{0}^\infty {\ln(a^2+x^2)\over{b^2+x^2}}dx$
49944
Integral $\int_1^3 \frac{\log x}{x^2+3}dx$
84884
Need help with the integral $\int_{0}^\infty e^{-x^{2}}x^{2n+1}dx $
107119
A logarithmic integral $\int^1_0 \frac{\log\left(\frac{1+x}{1-x}\right)}{x\sqrt{1-x^2}}\,dx$
65407
Evaluating $\int\limits_0^\infty \frac{\log x} {(1+x^2)^2} dx$ with residue theory
30731
Integral ${\frac{1}{\pi^2}} \int_{0}^{\infty}\frac{{(\ln{x}})^2}{\sqrt{x}{(1-x)^2}} \mathrm d x$
23087
Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis
24022
Compute $\int _0 ^{2\pi} (\sum_{n=1}^\infty \frac {\cos(nx)}{2^n})^2 dx$
68241
Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
102649
Prove that $\int_0^1\frac{x\ln (1+x)}{1+x^2}dx=\frac{\pi^2}{96}+\frac{\ln^2 2}{8}$
62840
Seemingly Simple Integral $\int_0^1\frac{x^2\ln x}{\sqrt{1-x^2}}dx$.
8358
Prove $\int_{0}^{\pi/2} \ln \left(x^{2} + (\ln\cos x)^2 \right) \, dx=\pi\ln\ln2 $