Evaluate: `intsin^2xcos^5x\ dx`

Explanation

To evaluate the integral \( \int \sin^2 x \cos^5 x \, dx \), we can use a substitution method that takes advantage of the odd power of cosine. Here’s a step-by-step solution:

### Step 1: Identify the odd power
We notice that \( \cos^5 x \) has an odd power. We can separate one \( \cos x \) from \( \cos^5 x \) to make the substitution easier.

\[ \int \sin^2 x \cos^5 x \, dx = \int \sin^2 x \cos^4 x \cos x \, dx \]
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