What is the integral from 1/2 to infinity of 1/(x^3) ?

The integral from 1/2 to infinity of 1/(x^3) is 2

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integral from 1/2 to infinity of 1/(x^3)

\int_{\frac{1}{2}}^{\infty} \frac{1}{x ^{3}} d x

2

Solution steps

\int_{\frac{1}{2}}^{\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_{\frac{1}{2}}^{\infty} \frac{1}{x ^{3}} d x = 0 - (- 2)

= 0 - (- 2)

Simplify

= 2

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What is the integral from 1/2 to infinity of 1/(x^3) ?
The integral from 1/2 to infinity of 1/(x^3) is 2