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

Explanation

To solve the integral \( I = \int \frac{1}{\sqrt{x+a} + \sqrt{x+b}} \, dx \), we will follow these steps:

### Step 1: Rationalize the Denominator
We start by multiplying and dividing the integrand by the conjugate of the denominator:

\[ I = \int \frac{\sqrt{x+a} - \sqrt{x+b}}{(\sqrt{x+a} + \sqrt{x+b})(\sqrt{x+a} - \sqrt{x+b})} \, dx \]
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