$\left(2x\right)dx+\left(y^2+1\right)dy=0$

$sin\left(x+\frac{\pi}{6}\right)=-\frac{\sqrt{3}}{2}$

$\frac{dy}{dx}\left(\frac{\left(x^2+5\right)}{x^2+6}\right)$

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

$\lim_{x\to3}\left(\frac{x^3-9x^2+27x-27}{2x^3-9x^2+27}\right)$

$\lim_{x\to0}\left(\frac{x^3+\sin^3\left(kx\right)}{x^2+\sin^2\left(kx\right)}\right)$

$\int\frac{12x^2+15x+7}{\left(x-2\right)\left(x+1\right)^2}dx$