What is the integral from 2 to infinity of x^{-1/3} ?

The integral from 2 to infinity of x^{-1/3} is diverges

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integral from 2 to infinity of x^{-1/3}

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

diverges

Solution steps

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

Compute the indefinite integral:

\int x^{- \frac{1}{3}} d x = \frac{3}{2} x^{\frac{2}{3}} + C

Compute the boundaries:

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

diverges

= diverges

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What is the integral from 2 to infinity of x^{-1/3} ?
The integral from 2 to infinity of x^{-1/3} is diverges