What is the integral from 0 to infinity of x^2ln(x) ?

The integral from 0 to infinity of x^2ln(x) is diverges

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integral from 0 to infinity of x^2ln(x)

\int_{0}^{\infty} x^{2} ln (x) d x

diverges

Solution steps

\int_{0}^{\infty} x^{2} ln (x) d x

Compute the indefinite integral:

\int x^{2} ln (x) d x = \frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9} + C

Compute the boundaries:

\int_{0}^{\infty} x^{2} ln (x) d x =

diverges

= diverges

\int_{0}^{1} 7 x^{3} (- x^{4} + 1)^{4} d x

\int_{- 7}^{7} 7 - ∣ x ∣ d x

\int_{0}^{π} x^{2} ∣ cos (x) ∣ d x

\int_{0}^{1} cos (3 x - 3) d x

\int_{1}^{3} \frac{x - 2}{x} d x

What is the integral from 0 to infinity of x^2ln(x) ?
The integral from 0 to infinity of x^2ln(x) is diverges