Contour integration of logarithmic functions: $\int_0^{\infty} \! \frac{\ln(x)}{x^2+a^2} \, \mathrm{d}x$
765
$\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues
45841
integral of $\int_{0}^{1}\frac{\ln(x^{2}+1)}{x+1}dx$ using contour integration?
46898
Fast calculation for $\int_{0}^{\infty}\frac{\log x}{x^2+1}dx=0$
140669
Evaluating the log gamma integral $\int_{0}^{z} \log \Gamma (x) \, \mathrm dx$ in terms of the Hurwitz zeta function
142516
Evaluating the integral, $\int_{0}^{\infty} \ln\left(1 - e^{-x}\right) \,\mathrm dx $
118324
Other challenging logarithmic integral $\int_0^1 \frac{\log^2(x)\log(1-x)\log(1+x)}{x}dx$
49944
Integral $\int_1^3 \frac{\log x}{x^2+3}dx$
108396
Integral $\int_0^{\infty} \frac{\log x}{\cosh^2x} \ \mathrm{d}x = \log\frac {\pi}4- \gamma$
68241
Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
157931
Contour integration of $\int \frac{dx} {(1+x^2)^{n+1}}$
109121
How to find integral of $\int_0^\infty \frac{\ln ^2z} {1+z^2}\mathrm{d}z$?
85949
Integral involving logarithm: $\int_0^\infty \frac{ \ln x}{(x+a)(x+b)} dx$
63167
Evaluate integral $\int_0^\frac{\pi}{2} \ln\left(\frac{1+a\cos x}{1-a\cos x}\right) \frac{\mathrm{d} x}{\cos x}$ for $\left|a\right|<1$
81914
Integrating $\int_0^1 \frac {\log(1-x)\log^2(1+x)}x \mathrm{d}x$
32672
Integrating :$\int_{0}^{1} \frac{x^{b}-x^{a}}{\log(x)}\sin(\log(x))dx$
146349
$\int_0^\infty \frac{\ln\left(1+x-\sqrt{2x}\right)}{1+x^2}\,dx$
79908
Show $\int_0^\infty \frac{e^{-x}-e^{-xt}}{x}dx = \ln(t),$ for $t \gt 0$