\(\displaystyle \int \frac{6x^2-4x-25}{x-2}  dx \) =

Summary Submit

Use long division or synthetic division:

$$ \begin{array}{r} 6x+8\phantom{-10} \\ x-2{\overline{\smash{\big)}\,6x^2-4x-25}} \\ \underline{-(6x^2-12x)} \hphantom{-9}\\ 8x-25\phantom{2} \\ \underline{-(8x-16)} \\ \end{array} $$ $$ \text{ Remainder}=-9 $$ $$ \int\frac{6x^2-4x-25}{x-2} = \int 6x+8 -\frac{9}{x-2} $$ $$ = \boxed{ 3x^2+8x-9\ln|x-2| + C} $$