$f\left(x\right)=x^3-\frac{1}{x^3}$

$3\pi\cdot8$

$\int xe^{-4x^2}dx$

$\frac{dy}{dx}=\sqrt{1+y^2}$

$3\:\cdot\:\:sin\:x^2\:-2\:\cdot\:\sqrt{2}\cdot\:\:sin\:x\:-\:cos\:x^2\:+1\:=0$

$\int_{-00}^{00}\left(\frac{1}{2x^2\left(x-1\right)}\right)dx$

$\sin\left(-\frac{\pi}{6}\right)\cos\left(\frac{\pi}{5}\right)+\cos\left(\frac{\pi}{6}\right)\sin\left(-\frac{\pi}{5}\right)$