$4x-8y+7+\frac{dy}{dx}=0$

$\int\left(\frac{14}{\left(x^2+1\right)^{\frac{3}{2}}}\right)dx$

$\left(\frac{1}{2}x^2+\frac{1}{2}y^2\right)^3$

$\int\sec^62xdx$

$\lim_{x\to0}\left(\frac{x}{\left(x^2+1\right)\left(x^3+1\right)}\right)$

$\int2tan^4\left(x\right)sec^6\left(x\right)dx$

$\frac{x^4+x^2+2}{x-2}$