Answer
$$\frac{3}{2} x^{2}+12 x-46 \ln |x-4|+C$$
Work Step by Step
Given $$\int \frac{\left(3 x^{2}-2\right) d x}{x-4}$$
By using long division, we get
\begin{aligned}
\frac{\left(3 x^{2}-2\right)}{x-4}= (3 x+12)-\frac{46}{x-4}
\end{aligned}
Then
\begin{aligned}
\int \frac{3 x^{2}-2}{x-4} d x &=\int(3 x-12) d x-\int \frac{46}{x-4} d x\\
&=\frac{3}{2} x^{2}+12 x-46 \ln |x-4|+C
\end{aligned}
