Integrate the rational functions`1/((e^x-1)`[Hint : Put `e^x=t`]

Explanation

To solve the integral \( I = \int \frac{1}{e^x - 1} \, dx \), we will follow the hint provided and use the substitution \( e^x = t \).

### Step-by-Step Solution:

1. **Substitution**: Let \( e^x = t \). Then, differentiate both sides to find \( dx \):
\[ \frac{d}{dx}(e^x) = e^x \implies dx = \frac{dt}{e^x} = \frac{dt}{t} \]
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