$6log\left(x\right)\:+\:2log\left(\:y\right)$

$\frac{d}{dx}x^2y+xy^2=5$

$\sin\left(x\right)+\frac{1}{\cot\left(x\right)}=\tan\left(x\right)\left(1+\cos\left(x\right)\right)$

$\sec x\tan x-5\csc^2x$

$x+7y=17$

$\int\frac{1}{6x^2+36x+78}dx$

$\frac{dy}{dx}=\frac{xy+3x-y-3}{4}$