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

$f\left(x\right)=\tan\left(a+a^3\right)$

$\frac{dy}{dx}+\cot\left(x\right)y=\frac{2}{sin\left(x\right)}$

$\lim_{x\to0}\left(x\left(\sin\left(\frac{8}{x}\right)+tan\:\left(\frac{2}{x}\right)\right)\right)$

$\left(y^{-1}+x^3\right)\left(y^{-1}-x^3\right)$

$\frac{d^2x}{d^2y}\left(7x^2+2y^2=4\right)$

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