`intx/(sqrt(x+a)-sqrt(x+b))dx`

Explanation

To solve the integral \( \int \frac{x}{\sqrt{x+a} - \sqrt{x+b}} \, dx \), we will follow a step-by-step approach:

### Step 1: Rationalizing the Denominator
We start by multiplying the numerator and denominator by the conjugate of the denominator:

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