c) Evaluate 

To evaluate the integral \(\int_{0}^{1} x^2 e^{3x} \, dx\), we can use integration by parts. 

Integration by parts formula is:
\[
\int u \, dv = uv - \int v \, du
\]

First, we choose \(u\) and \(dv\):
\[
u = x^2 \implies du = 2x \, dx
\]
\[
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