What is the integral from 0 to 3 of x^2ln(x) ?

The integral from 0 to 3 of x^2ln(x) is 9ln(3)-3

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integral from 0 to 3 of x^2ln(x)

\int_{0}^{3} x^{2} ln (x) d x

9 ln (3) - 3

Decimal Notation

6.88751 \dots

Solution steps

\int_{0}^{3} x^{2} ln (x) d x

Apply Integration By Parts

: [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{0}^{3}

= [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{0}^{3}

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

= [\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}]_{0}^{3}

Compute the boundaries:

9 ln (3) - 3

= 9 ln (3) - 3

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What is the integral from 0 to 3 of x^2ln(x) ?
The integral from 0 to 3 of x^2ln(x) is 9ln(3)-3