Integrate the functions`1/(xsqrt(a x-x))`

Explanation

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

### Step 1: Rewrite the Integral
We start with the integral:
\[ I = \int \frac{1}{x \sqrt{a x - x}} \, dx \]
We can factor out \( x \) from the square root in the denominator:
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