$\lim_{x\to2}\left(\frac{2^x-4}{3^x-9}\right)$

$\int\left(x^3\right)+2x-1\:\cos\left(4x\right)dx$

$\lim_{n\to\infty}\left(n\left(\sqrt{n^2+1}-n\right)\right)$

$x^2-12x+27$

$\frac{d}{dx}\sqrt[3]{\frac{1+x^2}{1-x^2}}$

$\int\frac{e^x}{\left(e^x-4\right)\left(e^x-2\right)}dx$