$\cos\left(2f\right)=\frac{\cot\left(f\right)-\tan\left(f\right)}{\cot\left(f\right)+\tan\left(f\right)}$

$\int\frac{e^{3t}+e^t}{\left(e^t-1\right)}dt$

$\int\frac{5y+3}{y^2\left(y+1\right)\left(y-3\right)}dy$

$\frac{x^4-3x^2+4}{x}$

$f\left(x\right)=4x-3x^5+2x^{-3}$

$\lim_{x\to3}\sqrt[3]{2x+2}$

$\int\frac{\left(x^3+4\right)}{\left(x^4+4x^2\right)}dx$