$\sin\left(x\right)\cdot\csc\left(40-x\right)=1$

$4x^2-12x-19$

$\frac{125-\frac{1}{512}x^{12}}{5-\frac{1}{8}x^4}$

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

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

$\int\frac{x^2\:+\:1}{x^3+3x+4}dx$

$\frac{x^{12}}{x^{12}}$