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

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

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integral of z^3ln(z)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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