Determine whether the improper integral ∫(x^(-1/3))dx converges or diverges.
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The given integral is: $$\int_{-\infty}^{\infty} \frac{x-1}{3} dx$$ Now, we can split this integral into two parts: $$\int_{-\infty}^{\infty} \frac{x-1}{3} dx = \int_{-\infty}^{0} \frac{x-1}{3} dx + \int_{0}^{\infty} \frac{x-1}{3} dx$$ Let's evaluate the first Show more…
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