To evaluate the integral \( \int x^2 e^{x^2} (2x) \, dx \), we can follow these steps:
### Step 1: Substitution
Let \( t = x^2 \). Then, we differentiate \( t \):
\[
dt = 2x \, dx \quad \Rightarrow \quad dx = \frac{dt}{2x}
\]
Since \( x^2 = t \), we can express \( x \) in terms of \( t \):
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