$\frac{dy}{dx}=\frac{2x}{3y^2},\:y\left(0\right)=20$

$\int\left(4x^3\sqrt{4x+7}\right)dx$

$81m^2-12x+9$

$\lim_{x\to\infty}\left(ln\left(5x^2+1\right)-2ln\left(4x+7\right)\right)$

$\left(\frac{xy^{-2}z^{-3}}{x^2y^3z^{-4}}\right)^{-3}$

$\tan^3\left(x+1\right)=\left(\tan\left(x+1\right)\right)\left(\sec^2\left(x\right)-\tan\left(x\right)\right)$

$\:\:\:\left(\frac{b+e}{c}\right)-\left(d+a\right)$