$\displaystyle \frac{6x^2 - 4x - 20}{x(x-4)(x+1)}dx$
I have no clue how to proceed from here. everything i try dosent look right.
Before starting integration, use partial fractions to decompose your term>
$\displaystyle \frac{6x^2 - 4x - 20}{x(x-4)(x+1)} = \frac{A}{x} + \frac{B}{x-4} + \frac{C}{x+1}$.....................(1)
or,
$\displaystyle {6x^2 - 4x - 20}= A(x-4)(x+1) + B (x)(x+1) + C (x)(x-4)$
find out A, B, and C. Plug them in equation (1) and then integrate!