What is the integral of [m^2ln(m)] ?

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

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integral of [m^2ln(m)]

\int [m^{2} ln (m)] d m

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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