What is the integral from-infinity to-1 of x^{-8/3} ?

The integral from-infinity to-1 of x^{-8/3} is diverges

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integral from-infinity to-1 of x^{-8/3}

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

diverges

Solution steps

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

Compute the indefinite integral:

\int x^{- \frac{8}{3}} d x = - \frac{3}{5 x ^{\frac{5}{3}}} + C

Compute the boundaries:

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

diverges

= diverges

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What is the integral from-infinity to-1 of x^{-8/3} ?
The integral from-infinity to-1 of x^{-8/3} is diverges