What is the integral from 0 to 7 of w^2ln(w) ?

The integral from 0 to 7 of w^2ln(w) is 343/3 ln(7)-343/9

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integral from 0 to 7 of w^2ln(w)

\int_{0}^{7} w^{2} ln (w) d w

\frac{343}{3} ln (7) - \frac{343}{9}

Decimal

184.37128 \dots

Solution steps

\int_{0}^{7} w^{2} ln (w) d w

Apply Integration By Parts

= [\frac{1}{3} w^{3} ln (w) - \int \frac{w ^{2}}{3} d w]_{0}^{7}

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

= [\frac{1}{3} w^{3} ln (w) - \frac{w ^{3}}{9}]_{0}^{7}

Compute the boundaries:

\frac{343}{3} ln (7) - \frac{343}{9}

= \frac{343}{3} ln (7) - \frac{343}{9}

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What is the integral from 0 to 7 of w^2ln(w) ?
The integral from 0 to 7 of w^2ln(w) is 343/3 ln(7)-343/9