$\int \frac {7x+1}{6x^2+x-1}\,dx$

so I evaluated the integral, but didn't seem to get the answer.

The answer the book suggests is $$\frac{2}{3} \ln {(3x-1)} + \frac {1}{2} \ln {(2x+1)} + C$$

but I've come to this thing: $$\frac{7}{12} [\ln {(3x-1)}+\ln {(2x+1)}-\frac{1}{12}\ln {\frac {x-\frac{1}{3}}{x+\frac{1}{2}}}]$$

Just help with simplification.

Thank you.