$\frac{4x^3\:-\:4x^2\:-\:8x}{2x\:-\:3}$

$\frac{d}{dx}\left(4e^xarctan\left(x\right)\right)$

$x+\frac{tanx}{sinx}$

$-x^3+11x^2-39x+45$

$\int\frac{x^2+3x}{\left(x-1\right)\left(x^2-2x+10\right)^{\frac{1}{2}}}dx$

$\frac{dy}{dx}+y=x^2+2x+1$

$\frac{sin\left(x\right)+sin\left(x\right)tan^2\left(x\right)}{tan\left(x\right)}$