How does one approach a integral such as this $\int _0^{\infty }\frac{\left(\ln x\right)^2}{\sqrt{x}\left(1-x\right)^2}\text{dx}$?
30731
Integral ${\frac{1}{\pi^2}} \int_{0}^{\infty}\frac{{(\ln{x}})^2}{\sqrt{x}{(1-x)^2}} \mathrm d x$
35861
Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
89499
Evaluating the integral $\int_0^{\frac{\pi}{2}}\log\left(\frac{1+a\cos(x)}{1-a\cos(x)}\right)\frac{1}{\cos(x)}dx$
93071
Is there a way to calculate the improper integral $\int_0^\infty \big(\frac{\ln x}{x - 1}\big)^2 dx$?
85618
Integral of $\frac{x^\alpha}{(1 + x^2)^2}$ from 0 to $\infty$ using contour integration for $-1 < \alpha <3$
140638
Integrating $\int_0^{\infty} \frac{dx}{1+x^3}$ using residues.
137625
Need a hint to evaluate the indefinite integral $\int\frac{e^x(2-x^2)}{(1-x)\sqrt{1-x^2}}dx$?
7388
Evaluate: $\int_0^{\pi} \ln \left( \sin \theta \right) d\theta$
45622
Value of this definite integral $\int_{0}^{\infty} \frac{ \ln(x)}{x^2+2x+4} dx $
74241
Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
77721
Is it possible to compute $\int_1^{+ \infty} \frac{dx}{x^2(1+e^x)}$?
85949
Integral involving logarithm: $\int_0^\infty \frac{ \ln x}{(x+a)(x+b)} dx$
121736
An improper integral : $\int_{0}^\infty {\ln(a^2+x^2)\over{b^2+x^2}}dx$
121310
Integral $\int_0^1 \log \left(\Gamma\left(x+\alpha\right)\right)\,{\rm d}x=\frac{\log\left( 2 \pi\right)}{2}+\alpha \log\left(\alpha\right) -\alpha$
114195
Evaluating $\int_0^\infty \frac{\log (1+x)}{1+x^2}dx$
98838
How to evaluate $\int_0^1 \frac{\ln(x+1)}{x^2+1} dx$
55738
Evaluating $\int _0^{\frac{\pi }{2}}\:\frac{\sqrt[3]{\sin^2\left(x\right)}}{\sqrt[3]{\sin^2\left(x\right)}+\sqrt[3]{\cos^2\left(x\right)}}dx$