$\left(4x+xy^2\right)\frac{dx}{dy}+x^2y=y$

$x^7+8y\frac{dy}{dx}=0$

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

$\sec\left(x\right)=\frac{1+\csc\left(x\right)}{\cot\left(x\right)+\cos\left(x\right)}$

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

$\frac{dy}{dx}=tan\left(x\right)sec\left(x\right)$

$\lim_{x\to\infty}\left(\frac{\sqrt{2x^2+3n-1}}{\sqrt{3n^2-n+4}}\right)$