$\frac{dv}{du}=cos\left(u+v\right)+cos\left(u-v\right)$

$\frac{15x^4-6xy^3}{\frac{3}{2}x}$

$\left(m+2\right)\left(m+6\right)-\left(m-4\right)^2$

$\left(\frac{\left(y^{2\:}+18\right)}{3}\right)^2$

$\lim_{x\to5}\left(-2x^2-2x+3\right)$

$\lim_{x\to0}\left(1-\cos^2\left(x\right)\right)$

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