What is the integral from 3 to infinity of 6/(x^3) ?

The integral from 3 to infinity of 6/(x^3) is 1/3

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integral from 3 to infinity of 6/(x^3)

\int_{3}^{\infty} \frac{6}{x ^{3}} d x

\frac{1}{3}

Decimal

0.33333 \dots

Solution steps

\int_{3}^{\infty} \frac{6}{x ^{3}} d x

Compute the indefinite integral:

\int \frac{6}{x ^{3}} d x = - \frac{3}{x ^{2}} + C

Compute the boundaries:

\int_{3}^{\infty} \frac{6}{x ^{3}} d x = 0 - (- \frac{1}{3})

= 0 - (- \frac{1}{3})

Simplify

= \frac{1}{3}

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What is the integral from 3 to infinity of 6/(x^3) ?
The integral from 3 to infinity of 6/(x^3) is 1/3