Evaluate: `inte^xsin^2x\ dx`

Explanation

To evaluate the integral \( I = \int e^x \sin^2 x \, dx \), we can use the identity for \( \sin^2 x \) and integration by parts. Here’s a step-by-step solution:

### Step 1: Rewrite \(\sin^2 x\)
We can use the trigonometric identity:
\[ \sin^2 x = \frac{1 - \cos(2x)}{2} \]
Thus, we rewrite the integral:
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