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Evaluate: int(x^2)/((x-1)^3(x+1))dx...

Evaluate: `int(x^2)/((x-1)^3(x+1))dx`

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To evaluate the integral \( \int \frac{x^2}{(x-1)^3 (x+1)} \, dx \), we will use the method of partial fractions. Here’s a step-by-step solution: ### Step 1: Set up the partial fractions We can express the integrand as a sum of simpler fractions: \[ \frac{x^2}{(x-1)^3 (x+1)} = \frac{A}{x-1} + \frac{B}{(x-1)^2} + \frac{C}{(x-1)^3} + \frac{D}{x+1} \] where \( A, B, C, D \) are constants to be determined. ...
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