$\int6x\cdot\cos\left(x\right)\cdot sin\left(x\right)dx$

$\frac{\csc\left(x\right)\cdot\sec\left(x\right)}{\cot\left(x\right)}=1+\tan^2\left(x\right)$

$w=xe^{\frac{y}{2}}$

$\frac{dy}{dx}+2y\:=\:y^3$

$\frac{dy}{dx}=6-\frac{2y}{3}$

$-7-\left(-1\right)-\left(-5\right)$

$\lim_{x\to0}\left(x^2+1\right)^{\frac{x^2+x+1}{x^3}}$