$\sqrt{1+x^2}\left(\frac{dy}{dx}\right)=\frac{x}{y}$

$4\left(x^2-10x\right)+4\left(y^2-6y\right)=-225$

$\lim_{x\to\infty}\left(x+32x^2-x+1\right)$

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

$\lim_{x\to0}\left(\frac{2-2\cos\left(5x\right)}{\sin\left(5x\right)}\right)$

$\frac{d}{dx}5^{4x}$

$\lim_{x\to0}\left(\frac{\left(e^{8x}-1-8x\right)}{x^2}\right)$