Evaluate: `intsin^(-1)sqrt(x/{a+x})\ dx`

Explanation

To evaluate the integral \( I = \int \sin^{-1} \left( \sqrt{\frac{x}{a+x}} \right) \, dx \), we will follow a systematic approach.

### Step 1: Substitution
Let us make the substitution:
\[ \sqrt{x} = \sin t \implies x = \sin^2 t \]
Then, differentiating both sides gives:
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