Simplify the expression $\frac{-8x^2\left(2-x^2\right)-3\left(2-x^2\right)^2-3x\left(2-x^2\right)^2}{3x\left(2-x^2\right)^2}$

Compute the integral

$\int xdx$

Compute the integral

$\int\left(x\cdot\cos\left(2x^2+3\right)\right)dx$

Compute the integral

$\int x\left(x^2-3\right)dx$

Compute the integral

$\int x^2\sin\left(x\right)dx$

Compute the integral

$\int x^2\cos\left(2x\right)dx$

Compute the integral

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

Compute the integral

$\int\left(\frac{x}{2}+3\right)^2dx$