$\lim_{x\to\infty}\left(\frac{e^{\frac{x}{12}}}{x}\right)$

$-\left(x+4\right)^2+12$

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

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

$\frac{y^{10}}{y^8}$

$\int\frac{5x+18}{x+4\cdot\left(x+3\right)}dx$

$\frac{d}{dx}\left(ln\left(\frac{\left(2t+1\right)^4}{\left(4t-1\right)^5}\right)\right)$