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

The integral of z^2ln(z) is 1/3 z^3ln(z)-(z^3)/9+C

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integral of z^2ln(z)

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

\frac{1}{3} z^{3} ln (z) - \frac{z ^{3}}{9} + C

Solution steps

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

Apply Integration By Parts

: \frac{1}{3} z^{3} ln (z) - \int \frac{z ^{2}}{3} d z

= \frac{1}{3} z^{3} ln (z) - \int \frac{z ^{2}}{3} d z

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

= \frac{1}{3} z^{3} ln (z) - \frac{z ^{3}}{9}

Add a constant to the solution

= \frac{1}{3} z^{3} ln (z) - \frac{z ^{3}}{9} + C

\int \frac{1}{3 x + x} d x

\int \frac{x ^{3}}{( 1 - x ^{2} ) ^{3}} d x

\int \frac{1}{( 1 + x + x ^{2} )} d x

\int (2 x^{3} - 1)^{2} d x

\int \frac{x ^{2}}{3 6 + x ^{3}} d x

What is the integral of z^2ln(z) ?
The integral of z^2ln(z) is 1/3 z^3ln(z)-(z^3)/9+C