$\frac{1+\coth\left(x\right)+\csc\left(x\right)}{1+\tan\left(x\right)+\sec\left(x\right)}$

$\lim_{x\to+\infty}\left(\frac{-\cos\left(x\right)}{x^2}\right)$

$\frac{x^4+2}{x^2+x+5}$

$\frac{11x-6x^3-9\:+12x^2}{3x^2-1}$

$10\ln\left(x^2+4\right)+8\ln\left(2x-5\right)$

$\frac{1+\cos\left(x\right)+\sin\left(x\right)}{1-\cos\left(x\right)^2-4\sin\left(x\right)^2+4\cos\left(x\right)\sin\left(x\right)}$

$\int\left(x^2\left(x^3-11\right)^9\right)dx$