Integrate the functions`1/(sqrt((x+a)(x+b))`

Explanation

To integrate the function \( \frac{1}{\sqrt{(x+a)(x+b)}} \), we can follow these steps:

### Step 1: Rationalize the Denominator
We start with the integral:
\[ I = \int \frac{1}{\sqrt{(x+a)(x+b)}} \, dx \]
To simplify this, we can multiply the numerator and the denominator by \( \sqrt{x+b} - \sqrt{x+a} \):
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