Integrate the function $e^x\left(e^x-2\right)\sqrt{3+e^x}$ from 0 to $\ln\left(6\right)$

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

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

Evaluate the integral

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

Evaluate the integral

$\int_{-1}^2\frac{3x}{x+4}dx$

Evaluate the integral

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

Evaluate the integral

$\int_9^4\left(\frac{x^2}{x+1}\right)dx$