$\frac{\cos\left(x\right)^2}{\sin\left(x\right)\left(1+\sin\left(x\right)\right)}$

$\frac{\left(12x^4+2x^3-3x^2+12x-9\right)}{4x^2+2x-3}$

$\frac{dy}{dx}=3y^{\frac{2}{3}};\:y\left(0\right)=0$

$3x^2-x+x^2+3x$

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

$f\left(x\right)=7x^{-3}-8x^{-5}$

$\frac{-1^n}{n^4\cdot n^{2n}}\cdot x^n$