Integrate the functions`(5x)/((x+1)(x^2+9)`

Explanation

To solve the integral of the function \( \frac{5x}{(x+1)(x^2+9)} \), we will use the method of partial fractions. Here’s the step-by-step solution:

### Step 1: Set Up Partial Fraction Decomposition
We start by expressing the integrand as a sum of partial fractions:
\[ \frac{5x}{(x+1)(x^2+9)} = \frac{A}{x+1} + \frac{Bx + C}{x^2 + 9} \]
where \( A \), \( B \), and \( C \) are constants that we need to determine.
...