Find the value of `int_(0)^(pi//2)cos^(5)x sin ^(7)xdx`

Explanation

To solve the integral \( I = \int_{0}^{\frac{\pi}{2}} \cos^5 x \sin^7 x \, dx \), we can use a substitution and properties of definite integrals.

### Step 1: Write the integral
We start with the integral:
\[ I = \int_{0}^{\frac{\pi}{2}} \cos^5 x \sin^7 x \, dx \]

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