After applying polynomial long division, I arrived at the following. Based on what is here, did I do this correctly?

$\displaystyle \int{x^2-2x+4}+\frac{-7}{3x+1}$

$\displaystyle \frac{1}{3}x^3-2*\frac{1}{2}x^2+4x-7\int\frac{1}{3x+1}$

$\displaystyle -7ln|3x+1|+C$