Simplify the expression $f\left(x\right)=etxtx^2-2x-3$

Compute the integral

$\int\:\frac{-x^2+8x^2-9x+2}{\left(x^2+1\right)\left(x-3\right)^2}dx$

Compute the integral

$\int xe^xdx$

Compute the integral

$\int\sin\left(x\right)^4dx$

Compute the integral

$\int\frac{x}{x^2+1}dx$

Evaluate the integral

$\int_0^2\left(x^4+2x^2-5\right)dx$

Compute the integral

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

Compute the integral

$\int e^x\cos\left(x\right)dx$