What is the integral from 0 to infinity of xln(x) ?

The integral from 0 to infinity of xln(x) is diverges

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integral from 0 to infinity of xln(x)

\int_{0}^{\infty} x ln (x) d x

diverges

Solution steps

\int_{0}^{\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_{0}^{\infty} x ln (x) d x =

diverges

= diverges

\int_{0}^{1} (8 x^{e} + 7 e^{x}) d x

\int_{- 5}^{0} 0 d x

\int_{1}^{2} ln (1 + x) d x

\int_{0}^{8} \frac{1}{2} x d x

\int_{- 3}^{3} \frac{2}{3} 9 - x^{2} d x

What is the integral from 0 to infinity of xln(x) ?
The integral from 0 to infinity of xln(x) is diverges