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Integrate the rational functionsx/((x^2...

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

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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. ### 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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