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

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

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

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

diverges

Solution steps

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

diverges

= diverges

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

\int_{1}^{4} 2 x + \frac{1}{x ^{2}} d x

\int_{0}^{t} sin (x) cos (t - x) d x

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

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

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