Integrate the rational functions`(5x)/((x+1)(x^2-4)`

Explanation

To solve the integral \(\int \frac{5x}{(x+1)(x^2-4)} \, dx\), we will use the method of partial fractions. Here’s a step-by-step solution:

### Step 1: Set up the partial fraction decomposition
We start by expressing the integrand as a sum of simpler fractions:
\[ \frac{5x}{(x+1)(x^2-4)} = \frac{Ax + B}{x^2 - 4} + \frac{C}{x + 1} \]
where \(A\), \(B\), and \(C\) are constants to be determined.
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