Integrate using partial fractions, identities and parts
All logarithms are natural and all angles are in radians. Construct the coefficients in the stated form; enter exact values
\[\int\frac{-4x-\frac{5}{2}}{(3x+1)(x-2)}\,dx\]
\[x\ne -\frac{1}{3},2\]
\[F(x)=P\log\left|3x+1\right|+Q\log\left|x-2\right|+C\]