$\int_{0}^{1} x\ln\left(x+1\right)dx$

$\int_2^3\frac{1}{\sqrt{x-1}}dx$

$\int_0^1\left(\frac{ln\left(x\right)}{x}\right)dx$

$\int_0^1\left(\frac{x}{\left(4-x^2\right)^{\frac{3}{2}}}\right)dx$

$\int_0^{\infty}\left(xe^{-x}\right)dx$

$\int_1^{\infty}\left(\frac{ln\left(x\right)}{x}\right)dx$

$\int_{-\infty}^0\left(xe^x\right)dx$

$\int_1^{\infty}\left(\frac{lnx}{x}\right)dx$