$a^2x^2-3by^2+2^2x^2-3by^2$

$2sin2x\:\left(1-2sin^2x\right)$

$\frac{dy}{dx}\left(ln\left(x^2+y^2\right)\right)$

$\lim_{x\to-1}\left(x+4\right)$

$cos2x\:+\:2\:cos\:x\:+\:1$

$\int x\left(x^2+7\right)^7dx$

$\int\frac{1}{2\cdot x^3}\cdot\left(1-\frac{1}{e^{\left(\frac{x}{5}\right)^3}}\right)dx$