What is the integral of z(ln(z))^2 ?

The integral of z(ln(z))^2 is 1/2 z^2ln^2(z)-1/2 z^2ln(z)+(z^2)/4+C

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integral of z(ln(z))^2

\int z (ln (z))^{2} d z

\frac{1}{2} z^{2} ln^{2} (z) - \frac{1}{2} z^{2} ln (z) + \frac{z ^{2}}{4} + C

Solution steps

\int z (ln (z))^{2} d z

Apply Integration By Parts

= \frac{1}{2} z^{2} ln^{2} (z) - \int z ln (z) d z

\int z ln (z) d z = \frac{1}{2} z^{2} ln (z) - \frac{z ^{2}}{4}

= \frac{1}{2} z^{2} ln^{2} (z) - (\frac{1}{2} z^{2} ln (z) - \frac{z ^{2}}{4})

Simplify

= \frac{1}{2} z^{2} ln^{2} (z) - \frac{1}{2} z^{2} ln (z) + \frac{z ^{2}}{4}

Add a constant to the solution

= \frac{1}{2} z^{2} ln^{2} (z) - \frac{1}{2} z^{2} ln (z) + \frac{z ^{2}}{4} + C

What is the integral of z(ln(z))^2 ?
The integral of z(ln(z))^2 is 1/2 z^2ln^2(z)-1/2 z^2ln(z)+(z^2)/4+C