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int (x)/((x^(2)+1)(x-1)) dx...


`int (x)/((x^(2)+1)(x-1)) dx`

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To solve the integral \( \int \frac{x}{(x^2 + 1)(x - 1)} \, dx \), we will use the method of partial fractions. Here is a step-by-step solution: ### Step 1: Set Up Partial Fraction Decomposition We start by expressing the integrand as a sum of partial fractions: \[ \frac{x}{(x^2 + 1)(x - 1)} = \frac{A}{x - 1} + \frac{Bx + C}{x^2 + 1} \] where \( A \), \( B \), and \( C \) are constants we need to determine. ...
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