$\frac{4\csc\:\left(2x\right)}{\sin\:\left(2x\right)}$

$\int5x^2\:dx$

$\int_0^{+\infty}\frac{-2}{x+2}dx$

$\frac{dy}{dx}\:=\:\frac{2xy}{y^2-x^2}$

$\frac{8x^5+4x^3+x^2+5x+16}{2x^3+x^2+3}$

$\int\left(9sec^3\left(2x\right)\right)dx$

$\lim_{x\to1}\left(\frac{\left(x+1\right)^{-1}-\left(2x\right)^{-1}}{x-1}\right)$