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
\[\int\frac{-\frac{5}{2}x+1}{(2x)(x-2)}\,dx\]
\[x\ne 0,2\]
\[F(x)=P\log\left|2x\right|+Q\log\left|x-2\right|+C\]