$\left(x^n-y^{2n}\right)\left(x^n+y^{2n}\right)$

$\left(t^2-12t+11\right)\frac{dy}{dx}=y$

$\int\frac{\left(e^{\ln\left(x\right)+3}\right)}{x}^7dx$

$\frac{dy}{dx}=\:2x+7$

$\int\:\:x^3\left(e^{-\frac{x}{3}}\right)dx$

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

$5x^2-20x+20$