$\lim_{x\to0}\left(\frac{x}{ctg\left(x\right)}\right)$

$\lim_{x\to\infty}\left(\left(\frac{5x-2}{5x+3}\right)^{5x+1}\right)$

$\int\left(2x\left(x^2+1\right)^{-5}\right)dx$

$\frac{dy}{dx}=\frac{y^{\ln\left(8e\right)}}{x^{\ln\left(2e\right)}}$

$e^{2x-y}+e^{y-2x}\cdot\frac{dy}{dx}$

$y-\frac{1}{3}\ge8$

$\int\:x^3cos\left(x^2\right)dx$