How do I prove that the integral ${\displaystyle\int_0^1}{\dfrac{\ln(x)}{1-x^2}dx}$ converges?
116498
Convergence of improper integral $\int_{0}^{1}\frac{\log(x)}{1-x^2}dx$
63756
Convergence or divergence of the integral $\int\limits_{10}^\infty \frac{e^x}{x^{1 + \frac{1}{x}} (e^x -1)} \,dx$
63956
Evaluate $\int_0^{\infty}\frac{\ln x}{x^a(x+1)}dx$ where $0<a<1$
98836
Showing $\int_x^{x+1}f(t)\,dt \xrightarrow{x\to\infty}0$ for $f\in L^2 (\mathbb{R})$
97083
Convergences of definite integral of a function
21375
The integral $\int_0^\infty \dfrac{x \sin(x)}{x^2+1} dx$
93071
Is there a way to calculate the improper integral $\int_0^\infty \big(\frac{\ln x}{x - 1}\big)^2 dx$?
105707
A proof of $\int_{0}^{1}\left( \frac{\ln t}{1-t}\right)^2\,\mathrm{d}t=\frac{\pi^2}{3}$
141926
A Challenging Logarithmic Integral $\int_0^1 \frac{\log(x)\log(1-x)\log^2(1+x)}{x}dx$
10408
Uniformly convergence of $f_{n+1}(x)= \int^x_0 f_n(t)dt$
152648
Is the integral $\int_1^\infty\frac{x^{-a} - x^{-b}}{\log(x)}\,dx$ convergent?
122971
how to prove that $\ln(1+x)< x$
38567
Convergence $I=\int_0^\infty \frac{\sin x}{x^s}dx$
45622
Value of this definite integral $\int_{0}^{\infty} \frac{ \ln(x)}{x^2+2x+4} dx $
124916
$f$ such that $\int_1^{\infty}f(x)dx$ converges, but not absolutely?
11435
Show that $\sum_{k=1}^\infty \frac{\ln{k}}{k^2}$ converges or diverges
88792
Convergence of $\int_0^\infty $sin$ (x^p) dx$