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

The integral from 2 to infinity of x^{-3} is 1/8

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

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

\frac{1}{8}

Decimal Notation

0.125

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{2}^{\infty} x^{- 3} d x = 0 - (- \frac{1}{8})

= 0 - (- \frac{1}{8})

Simplify

= \frac{1}{8}

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What is the integral from 2 to infinity of x^{-3} ?
The integral from 2 to infinity of x^{-3} is 1/8