What is the integral from 3 to infinity of xln(x) ?

The integral from 3 to infinity of xln(x) is diverges

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integral from 3 to infinity of xln(x)

\int_{3}^{\infty} x ln (x) d x

diverges

Solution steps

\int_{3}^{\infty} x ln (x) d x

Compute the indefinite integral:

\int x ln (x) d x = \frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4} + C

Compute the boundaries:

\int_{3}^{\infty} x ln (x) d x =

diverges

= diverges

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What is the integral from 3 to infinity of xln(x) ?
The integral from 3 to infinity of xln(x) is diverges