$\int_0^4\frac{\log x}{\sqrt{4x-x^2}} dx=0$
50509
Prove that $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}}~dx=0$ (without trigonometric substitution)
132452
Integral $\int_{\frac{1}{2}}^1 \frac{\ln x}{\sqrt{x^2+1}}dx$
108357
Integral $\int_0^\infty \log^2 x\frac{1+x^2}{1+x^4}dx=\frac{3 \pi^3}{16\sqrt 2}$
45622
Value of this definite integral $\int_{0}^{\infty} \frac{ \ln(x)}{x^2+2x+4} dx $
91333
How to find $\int_{0}^{1}\dfrac{\ln^2{x}\ln^2{(1-x)}}{2-x}dx$
59352
Computing: $\int_0^1 \sqrt[3]{x\log{\frac{1}x}} \, \mathrm dx$
155919
Integral $\small \int_0^\infty \frac{(\pi x - 2\log{x})^3}{\left(\log^2{x} + \frac{\pi^2}{4}\right)(1+x^2)^2} \text{d}x$
147108
Prove that $\int_0^\infty \frac{x\,\log x}{(1+x^2)^2} = 0$
68241
Integral $\int_0^1 \frac{\ln(1-x)\ln(1+x^2)}{x}dx$
17996
Integral $\int_0^1 \frac{\ln(x+\sqrt{1-x^2})}{x}dx$
21464
Finding the integral $\int_0^1 \frac{x^a - 1}{\log x} dx$
92637
Evaluating $\int \frac{\operatorname dx}{x\log x}$
23087
Evaluate $\int_0^\infty \frac{(\log x)^2}{1+x^2} dx$ using complex analysis
89499
Evaluating the integral $\int_0^{\frac{\pi}{2}}\log\left(\frac{1+a\cos(x)}{1-a\cos(x)}\right)\frac{1}{\cos(x)}dx$
117587
$\int_{0}^{1}\frac{\sin^{-1}\sqrt x}{x^2-x+1}dx$
81914
Integrating $\int_0^1 \frac {\log(1-x)\log^2(1+x)}x \mathrm{d}x$
765
$\int_0^\infty \frac{\log(x)}{x^2+\alpha^2}$ using residues