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Integrate the rational functions1/(x(x^...

Integrate the rational functions`1/(x(x^4-1)`

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To solve the integral \( \int \frac{1}{x(x^4 - 1)} \, dx \), we will follow these steps: ### Step 1: Factor the Denominator The denominator can be factored as: \[ x^4 - 1 = (x^2 - 1)(x^2 + 1) = (x - 1)(x + 1)(x^2 + 1) \] Thus, we rewrite the integral: ...
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