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

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

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integral from 1 to infinity of x^n

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

diverges

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

diverges

= diverges

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