What is the integral from 1 to 5 of w^2ln(w) ?

The integral from 1 to 5 of w^2ln(w) is -124/9+125/3 ln(5)

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integral from 1 to 5 of w^2ln(w)

\int_{1}^{5} w^{2} ln (w) d w

- \frac{124}{9} + \frac{125}{3} ln (5)

Decimal

53.28213 \dots

Solution steps

\int_{1}^{5} w^{2} ln (w) d w

Apply Integration By Parts

= [\frac{1}{3} w^{3} ln (w) - \int \frac{w ^{2}}{3} d w]_{1}^{5}

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

= [\frac{1}{3} w^{3} ln (w) - \frac{w ^{3}}{9}]_{1}^{5}

Compute the boundaries:

- \frac{124}{9} + \frac{125}{3} ln (5)

= - \frac{124}{9} + \frac{125}{3} ln (5)

What is the integral from 1 to 5 of w^2ln(w) ?
The integral from 1 to 5 of w^2ln(w) is -124/9+125/3 ln(5)