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int(0)^(1)x e^(x^(2)) dx...

`int_(0)^(1)x e^(x^(2)) dx`

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To solve the integral \( I = \int_{0}^{1} x e^{x^2} \, dx \), we will use substitution. ### Step 1: Substitution Let \( t = x^2 \). Then, differentiating both sides gives: \[ dt = 2x \, dx \quad \Rightarrow \quad x \, dx = \frac{dt}{2} \] ...
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