Find the following integral (using partial fraction method)
`int dx/(x(x^2+8))`

Explanation

To solve the integral \( \int \frac{dx}{x(x^2 + 8)} \) using the method of partial fractions, we will follow these steps:

### Step 1: Set up the partial fraction decomposition
We start by expressing the integrand in terms of partial fractions:
\[ \frac{1}{x(x^2 + 8)} = \frac{A}{x} + \frac{Bx + C}{x^2 + 8} \]
where \( A \), \( B \), and \( C \) are constants that we need to determine.
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