$\frac{12x^3+10x^2+11x+12}{3x+1}$

$\frac{d}{dx}xy\:\log x=1$

$\lim_{x\to\infty}\left(8xe^{\frac{1}{x}}-8x\right)$

$\lim_{x\to5}\left(\frac{\ln\left(x-4\right)}{x^2-25}\right)dx$

$\frac{-4+0\:0\:-4}{1}$

$\int\frac{\ln\left(2+\sqrt[3]{x}\right)}{\sqrt[3]{x}}dx$

$9m^44mn+4n^2$