Evaluate the definite integrals`int_0^1x e^(x^2)dx`

Explanation

To evaluate the definite integral \( \int_0^1 x e^{x^2} \, dx \), we can use the method of substitution. Here are the steps to solve the integral:

### Step 1: Choose a substitution
Let \( t = x^2 \). Then, we differentiate both sides to find \( dt \):
\[ dt = 2x \, dx \quad \Rightarrow \quad dx = \frac{dt}{2x} \]

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