What is the integral from 2 to infinity of 1/(x^3-8) ?

The integral from 2 to infinity of 1/(x^3-8) is diverges

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integral from 2 to infinity of 1/(x^3-8)

\int_{2}^{\infty} \frac{1}{x ^{3} - 8} d x

diverges

Solution steps

\int_{2}^{\infty} \frac{1}{x ^{3} - 8} d x

Compute the indefinite integral:

\int \frac{1}{x ^{3} - 8} d x = \frac{1}{12} ln ∣ x - 2 ∣ - \frac{1}{24} ln x^{2} + 2 x + 4 - \frac{1}{4 3} arctan (\frac{1}{3} (x + 1)) + C

Compute the boundaries:

\int_{2}^{\infty} \frac{1}{x ^{3} - 8} d x =

diverges

= diverges

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What is the integral from 2 to infinity of 1/(x^3-8) ?
The integral from 2 to infinity of 1/(x^3-8) is diverges