$\frac{dy}{dx}\left(y\:=\:x\sqrt{x^2\:+\:41}\right)$

$\frac{2t+1}{t+3}>3$

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

$\:\frac{\sqrt{x^{-2}y^5+\:x^{-5}y^4}}{x^4\:y^4}\quad$

$\left(\frac{1}{2x}+\frac{1}{3y^2}\right)\left(\frac{1}{2x}-\frac{1}{3y^2}\right)$

$\frac{cosxcotx}{sinx}+1$

$\int2x^4\left(2x^3-5x^4\right)dx$