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

The integral from 1 to 2 of x^2*ln(x) is -7/9+8/3 ln(2)

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

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

- \frac{7}{9} + \frac{8}{3} ln (2)

Decimal Notation

1.07061 \dots

Solution steps

\int_{1}^{2} 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}^{2}

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

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

= [\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}]_{1}^{2}

Compute the boundaries:

- \frac{7}{9} + \frac{8}{3} ln (2)

= - \frac{7}{9} + \frac{8}{3} ln (2)

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What is the integral from 1 to 2 of x^2*ln(x) ?
The integral from 1 to 2 of x^2*ln(x) is -7/9+8/3 ln(2)