Evaluate: `int(sin^(-1)x)^3\ dx`

Explanation

To evaluate the integral \( I = \int (\sin^{-1} x)^3 \, dx \), we will use integration by parts and a substitution method. Here are the steps:

### Step 1: Substitution
Let \( \theta = \sin^{-1} x \). Then, we have:
\[ x = \sin \theta \quad \text{and} \quad dx = \cos \theta \, d\theta \]
Now, we can rewrite the integral in terms of \( \theta \):
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