What is the integral from 1 to infinity of x^{-6} ?

The integral from 1 to infinity of x^{-6} is 1/5

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integral from 1 to infinity of x^{-6}

\int_{1}^{\infty} x^{- 6} d x

\frac{1}{5}

Decimal

0.2

Solution steps

\int_{1}^{\infty} x^{- 6} d x

Compute the indefinite integral:

\int x^{- 6} d x = - \frac{1}{5 x ^{5}} + C

Compute the boundaries:

\int_{1}^{\infty} x^{- 6} d x = 0 - (- \frac{1}{5})

= 0 - (- \frac{1}{5})

Simplify

= \frac{1}{5}

What is the integral from 1 to infinity of x^{-6} ?
The integral from 1 to infinity of x^{-6} is 1/5