Find the indicated integrals (if they exist)

$\displaystyle \int x^2\sqrt{3 x + 6}\,dx$ =

$\displaystyle \int_{-\infty}^{\infty} \frac{e^{6 x}}{e^{12 x}+1}\,dx$ =

$\displaystyle \int \frac{4 x + 7}{3 x^2 + 19 x + 6}\,dx$ =

$\displaystyle \int \frac{\ln(x)}{x^{5}}\,dx$ =