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

$\left(3y+x\right)\left(3y-x\right)$

$-xydx+\left(x^2-2xy\right)dy=0$

$\int\frac{5x-25}{x^3-7x^2+20x-24}dx$

$\int\frac{10x^6-4x^2-15x+16}{x}dx$

$\frac{dy}{dx}\left(y=4x^{-3}+7x^{-1}+5\right)$

$\int\sqrt[5]{x^4-x^2}\left(12x^3-6x\right)dx$