Answer
$$ \frac{4}{5}x^5 -3x^4 + 3x^3+c$$
Work Step by Step
\begin{align*}
\int\left(2 x^{2}-3 x\right)^{2} d x&= \int\left(4 x^{4}-12 x^3 +9x^2\right) d x\\
&= \frac{4}{5}x^5 -3x^4 + 3x^3+c
\end{align*}
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