Integrate the function $x^2\sqrt{2x^2+1+x^4}\ln\left(x\right)$ from $1$ to $3$

Evaluate the integral

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

Evaluate the integral

$\int_1^exlnx\:dx$

Evaluate the integral

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

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

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