$\sin\left(6\pi\left(1-w\right)\right)=\sin\left(6\pi w\right)$

$\:4x^{4n}-16y^{2m}$

$\left(4x^2-1\right)x\left(x^3-3x^2+6x-2\right)$

$\int\frac{1}{x^2\sqrt{x^2-8}}dx$

$\lim_{x\to0}\left(\frac{-3}{1-3x}\right)$

$\lim_{x\to\infty}\left(\ln\left(x\right)-\ln\left(x+1\right)\right)$

$\frac{dy}{dx}=\frac{3x^2+2x}{4y-5}$