What is the integral from 1 to infinity of x^p ?

The integral from 1 to infinity of x^p is diverges

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integral from 1 to infinity of x^p

\int_{1}^{\infty} x^{p} d x

diverges

Solution steps

\int_{1}^{\infty} x^{p} d x

Compute the indefinite integral:

\int x^{p} d x = \frac{x ^{p + 1}}{p + 1} + C

Compute the boundaries:

\int_{1}^{\infty} x^{p} d x =

diverges

= diverges

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What is the integral from 1 to infinity of x^p ?
The integral from 1 to infinity of x^p is diverges