$\frac{x^3-3x+2}{x^3+x^2-2x}$

$\lim_{x\to1}\left(\frac{3x^3-3x}{-x+1}\right)$

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

$\lim_{x\to\infty}\left(\log\left(x^2-4\right)\right)$

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

$16x^2x+48yx+36y^2$

$\lim_{x\to0}\left(\frac{\left(e^x-e^{-x}-2\right)}{1-cos2x}\right)$