Evaluating the definite integral $\int_0^{\infty} \frac{(\ln x)^2}{x^2 + 1} dx$
23087
Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis
765
$\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues
16775
Showing that $\int_{0}^{\infty} \frac{dx}{1 + x^2} = 2 \int_0^1 \frac{dx}{1 + x^2}$
62840
Seemingly Simple Integral $\int_0^1\frac{x^2\ln x}{\sqrt{1-x^2}}dx$.
59667
Evaluating $\int_0^\infty\frac{\sin(x)}{x^2+1}\, dx$
83325
Integral of $\frac{\sqrt{x^2+1}}{x}$
45622
Value of this definite integral $\int_{0}^{\infty} \frac{ \ln(x)}{x^2+2x+4} dx $
30731
Integral ${\frac{1}{\pi^2}} \int_{0}^{\infty}\frac{{(\ln{x}})^2}{\sqrt{x}{(1-x)^2}} \mathrm d x$
115598
Evaluating $\int_{0}^{1} dx\frac{\log(1+x)}{1 + x^2}$
132388
Calculate $I=\int_0^1\frac{\ln(1+x)}{1+x^2}\,dx$
24716
$\int_0^\infty\frac{\log x dx}{x^2-1}$ with a hint.
74241
Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$
81831
Evaluate $\int_0^{\infty}\frac{\log x}{1+e^x}\,dx$
86923
Evaluating the integral $\int_0^\infty \frac{x \sin rx }{a^2+x^2} dx$ using only real analysis
57463
Evaluate the integral using the theory of residues: $\int_{-\infty}^{\infty} \frac{dx}{(x^2+1)^2(x^2+16)}$
138174
Integral $\int_0^1 \frac{x\ln\left(\frac{1+x}{1-x}\right)}{\left(\pi^2+\ln^2\left(\frac{1+x}{1-x}\right)\right)^2}dx$
93071
Is there a way to calculate the improper integral $\int_0^\infty \big(\frac{\ln x}{x - 1}\big)^2 dx$?