This particular problem has been giving me trouble, and while the math dept tutors did help a great deal, the resulting answer hasn't been accepted by the online homework submission website. Find the definite integral of
$$\int\frac{x(x+1)}{2x^{3}+3x^{2}-13}$$
The work done so far with the help of the tutors is
$$\int\frac{x(x+1)}{2x^{3}+3x^{2}-13} = \int\frac{x^{2}+x}{2x^{3}+3x^{2}-13}$$
Let u=$2x^{3}+3x^{2}-13$
and ${u}'= 6x^{2}+6x = 6(x^{2}+x)$
$$\int\frac{1}{6}\cdot\frac{{u}'}{u}= \frac{1}{6}\int\frac{{u}'}{u}$$ $$\frac{1}{6}\ln~u= \frac{1}{6}\ln(2x^{3}+3x^{2}-13)+C$$
What is missing from this solution?