Solve the equation $\frac{d^2}{dx^2}\left(y\right)+\left(1+x^2\right)y=0$

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

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