Integrate the function $x\ln\left(x\right)$ from $1$ to $2$

Evaluate the integral

$\int_0^1\left(\ln\left(1+x\right)\right)dx$

Evaluate the integral

$\int_1^exlnx\:dx$

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

$\int_1^2x\ln\left(x\right)dx$

Evaluate the integral

$\int_0^3\sqrt{9-x^2}dx$