Integrate the function $\mathrm{arcsec}\left(\sqrt{t}\right)$ from $2$ to $4$

Evaluate the integral

$\int_0^1xln\left(x\right)dx$

Evaluate the integral

$\int_1^exlnx\:dx$

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

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

Evaluate the integral

$\int_{-\infty}^0xe^xdx$