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

Explanation

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

### Step 1: Set up the partial fraction decomposition
We can express the integrand as:
\[ \frac{x}{(x^2 + 1)(x - 1)} = \frac{Ax + B}{x^2 + 1} + \frac{C}{x - 1} \]
where \( A, B, \) and \( C \) are constants that we need to determine.
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