$\int_{\frac{\pi}{3}}^{\frac{\pi}{4}}\left(-cot^2x\right)dx$

$-\frac{3x}{3x^2-3}$

$\int\:\:\frac{1-2x^3}{x^5+x^3}dx$

$7\:sin\left(2x\right)\:=\:7\:cos\left(x\right)$

$\frac{2}{5-x}+\frac{3}{x+7}=1$

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

$\frac{x^3+2x+3}{x+1}$