$\log_b\:3-\log_b\:3$

$\frac{2x^3}{3+4x^2}$

$\int\:\frac{8}{x\left(7+12\ln\:\left(x\right)\right)^9}dx$

$axy+3axy+3xyz+axy$

$\frac{dq}{dp}\:lnq^3=\:ln\left[\left(p-2\right)^{\frac{1}{2}}\:\right]\left(p^2-1\right)\left(p^4+6\right)$

$\frac{d}{dx}\left(\log\left(sin^2\left(4x\right)\right)\right)$

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