Evaluate: (i) `int(a^x)/(sqrt(1-a^(2x)))\ dx`

Explanation

To evaluate the integral \( I = \int \frac{a^x}{\sqrt{1 - a^{2x}}} \, dx \), we will follow these steps:

### Step 1: Substitution
Let \( t = a^x \). Then, differentiating both sides with respect to \( x \), we get:
\[ \frac{dt}{dx} = a^x \ln a \implies dt = a^x \ln a \, dx \implies dx = \frac{dt}{a^x \ln a} = \frac{dt}{t \ln a} \]

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