What is the integral from 5 to infinity of 1/(x^9) ?

The integral from 5 to infinity of 1/(x^9) is 1/3125000

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integral from 5 to infinity of 1/(x^9)

\int_{5}^{\infty} \frac{1}{x ^{9}} d x

\frac{1}{3125000}

Decimal

0.00000032

Solution steps

\int_{5}^{\infty} \frac{1}{x ^{9}} d x

Compute the indefinite integral:

\int \frac{1}{x ^{9}} d x = - \frac{1}{8 x ^{8}} + C

Compute the boundaries:

\int_{5}^{\infty} \frac{1}{x ^{9}} d x = 0 - (- \frac{1}{3125000})

= 0 - (- \frac{1}{3125000})

Simplify

= \frac{1}{3125000}

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What is the integral from 5 to infinity of 1/(x^9) ?
The integral from 5 to infinity of 1/(x^9) is 1/3125000