What is the integral from 1 to infinity of 1/(x^7) ?

The integral from 1 to infinity of 1/(x^7) is 1/6

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integral from 1 to infinity of 1/(x^7)

\int_{1}^{\infty} \frac{1}{x ^{7}} d x

\frac{1}{6}

Decimal Notation

0.16666 \dots

Solution steps

\int_{1}^{\infty} \frac{1}{x ^{7}} d x

Compute the indefinite integral:

\int \frac{1}{x ^{7}} d x = - \frac{1}{6 x ^{6}} + C

Compute the boundaries:

\int_{1}^{\infty} \frac{1}{x ^{7}} d x = 0 - (- \frac{1}{6})

= 0 - (- \frac{1}{6})

Simplify

= \frac{1}{6}

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What is the integral from 1 to infinity of 1/(x^7) ?
The integral from 1 to infinity of 1/(x^7) is 1/6