What is the integral from 3 to infinity of 1/(x^3) ?

The integral from 3 to infinity of 1/(x^3) is 1/18

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integral from 3 to infinity of 1/(x^3)

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

\frac{1}{18}

Decimal Notation

0.05555 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{3}^{\infty} \frac{1}{x ^{3}} d x = 0 - (- \frac{1}{18})

= 0 - (- \frac{1}{18})

Simplify

= \frac{1}{18}

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What is the integral from 3 to infinity of 1/(x^3) ?
The integral from 3 to infinity of 1/(x^3) is 1/18