What is the integral from 1 to 3 of x^2*ln(x) ?

The integral from 1 to 3 of x^2*ln(x) is 9ln(3)-26/9

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integral from 1 to 3 of x^2*ln(x)

\int_{1}^{3} x^{2} \cdot ln (x) d x

9 ln (3) - \frac{26}{9}

Decimal

6.99862 \dots

Solution steps

\int_{1}^{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]_{1}^{3}

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

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

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

Compute the boundaries:

9 ln (3) - \frac{26}{9}

= 9 ln (3) - \frac{26}{9}

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What is the integral from 1 to 3 of x^2*ln(x) ?
The integral from 1 to 3 of x^2*ln(x) is 9ln(3)-26/9