What is the integral of w^3ln(w) ?

The integral of w^3ln(w) is 1/4 w^4ln(w)-(w^4)/(16)+C

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integral of w^3ln(w)

\int w^{3} ln (w) d w

\frac{1}{4} w^{4} ln (w) - \frac{w ^{4}}{16} + C

Solution steps

\int w^{3} ln (w) d w

Apply Integration By Parts

: \frac{1}{4} w^{4} ln (w) - \int \frac{w ^{3}}{4} d w

= \frac{1}{4} w^{4} ln (w) - \int \frac{w ^{3}}{4} d w

\int \frac{w ^{3}}{4} d w = \frac{w ^{4}}{16}

= \frac{1}{4} w^{4} ln (w) - \frac{w ^{4}}{16}

Add a constant to the solution

= \frac{1}{4} w^{4} ln (w) - \frac{w ^{4}}{16} + C

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What is the integral of w^3ln(w) ?
The integral of w^3ln(w) is 1/4 w^4ln(w)-(w^4)/(16)+C