How to calculate the integral $I=\int\limits_0^1\frac{x^n-1}{\ln(x)} \,\mathrm dx$
30030
An integration question to be solved without using differentiation under the integral sign.
53830
Evaluate $ \int_{0}^{1} \ln(x)\ln(1-x)\,dx $
114372
Calculate $\lim_{t\to\infty}\frac 1t\log\int_0^1 \cosh(tf(x))\mathrm d x$
138169
Finding $\lim\limits_{n \to \infty }n\int_{0}^{1}\frac{x^{n}}{1+x+x^{n}}dx$
19716
What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$?
53566
Proving $\int_0^1 \frac{(\ln(x))^5}{1+x} \mathrm{d}x = -\frac{31\pi^6}{252}$
84884
Need help with the integral $\int_{0}^\infty e^{-x^{2}}x^{2n+1}dx $
41416
Integrating $ \int_2^4 \frac{ \sqrt{\ln(9-x)} }{ \sqrt{\ln(9-x)}+\sqrt{\ln(x+3)} } dx. $
115198
Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$
123802
Is the integral of $\frac{1}{x}$ equal to $\ln(x)$ or $\ln(|x|)$?
30731
Integral ${\frac{1}{\pi^2}} \int_{0}^{\infty}\frac{{(\ln{x}})^2}{\sqrt{x}{(1-x)^2}} \mathrm d x$
106812
Find $\int_{0}^{\infty} \frac{\ln(x)}{1+x^2}dx$
53519
Finding $\int_0^1{\frac{x^4(1-x)^4}{1+x^2}}dx$
35861
Evaluate $\int_0^\infty\frac{\ln x}{1+x^2}dx$
139784
Computing integration $\int_0^1\frac{\ln x}{1-x}d x$
109887
How to evaluate $\int_0^1 (\arctan x)^2 \ln(\frac{1+x^2}{2x^2}) dx$
101045
Is there a closed form for the integral $\int_0^1 x^n \log^m (1-x) \, {\rm d}x$?