What is the integral from 2 to infinity of 5/(x^3) ?

The integral from 2 to infinity of 5/(x^3) is 5/8

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integral from 2 to infinity of 5/(x^3)

\int_{2}^{\infty} \frac{5}{x ^{3}} d x

\frac{5}{8}

Decimal

0.625

Solution steps

\int_{2}^{\infty} \frac{5}{x ^{3}} d x

Compute the indefinite integral:

\int \frac{5}{x ^{3}} d x = - \frac{5}{2 x ^{2}} + C

Compute the boundaries:

\int_{2}^{\infty} \frac{5}{x ^{3}} d x = 0 - (- \frac{5}{8})

= 0 - (- \frac{5}{8})

Simplify

= \frac{5}{8}

What is the integral from 2 to infinity of 5/(x^3) ?
The integral from 2 to infinity of 5/(x^3) is 5/8