14) \( \int \frac{x}{x^{3}-1} d x \)
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The denominator suggests a factorization might be helpful. Recall that \(x^3 - 1\) can be factored using the difference of cubes formula: \(a^3 - b^3 = (a - b)(a^2 + ab + b^2)\). Here, \(a = x\) and \(b = 1\), so \(x^3 - 1 = (x - 1)(x^2 + x + 1)\). Show more…
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