What is the integral from 0 to infinity of x^n ?

The integral from 0 to infinity of x^n is diverges

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integral from 0 to infinity of x^n

\int_{0}^{\infty} x^{n} d x

diverges

Solution steps

\int_{0}^{\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_{0}^{\infty} x^{n} d x =

diverges

= diverges

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\int_{0}^{1} \frac{8}{t ^{2} + 1} d t

\int_{5}^{x^{2}} \frac{1}{t ^{5}} d t

What is the integral from 0 to infinity of x^n ?
The integral from 0 to infinity of x^n is diverges