What is the integral from 1 to infinity of 1/(x^{13/12)} ?

The integral from 1 to infinity of 1/(x^{13/12)} is 12

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integral from 1 to infinity of 1/(x^{13/12)}

\int_{1}^{\infty} \frac{1}{x ^{\frac{13}{12}}} d x

12

Solution steps

\int_{1}^{\infty} \frac{1}{x ^{\frac{13}{12}}} d x

Compute the indefinite integral:

\int \frac{1}{x ^{\frac{13}{12}}} d x = - \frac{12}{x ^{\frac{1}{12}}} + C

Compute the boundaries:

\int_{1}^{\infty} \frac{1}{x ^{\frac{13}{12}}} d x = 0 - (- 12)

= 0 - (- 12)

Simplify

= 12

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What is the integral from 1 to infinity of 1/(x^{13/12)} ?
The integral from 1 to infinity of 1/(x^{13/12)} is 12