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Integrate the rational functions(3x+5)/...

Integrate the rational functions`(3x+5)/(x^3-x^2-x+1)`

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To solve the integral of the rational function \(\frac{3x + 5}{x^3 - x^2 - x + 1}\), we will follow these steps: ### Step 1: Factor the Denominator We start with the denominator \(x^3 - x^2 - x + 1\). We can factor this expression. 1. **Factor by grouping**: \[ x^3 - x^2 - x + 1 = x^2(x - 1) - 1(x - 1) = (x^2 - 1)(x - 1) ...
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