$\frac{d}{dx}\sqrt{xy}=x^4y+30$

$\frac{297}{-33}$

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

$\int\frac{6+10x}{x^2-4}dx$

$\lim_{x\to0}\left(\frac{e^{xb}-e^{xa}}{x\left(b-a\right)}\right)$

$\left[\frac{\sqrt[3]{27a\:}\:\sqrt{b^{-3}\:a^{-\frac{1}{3\:}}\:b}}{\sqrt{b^{-1}}\sqrt{16a^2}}\right]^{-1}$

$\int6t\sin\left(3t^2\right)dt$