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

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

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integral of y^2ln(y)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int \frac{x + 1}{x ^{2} - x + 1} d x

x \to 0 lim (x + x)

\int 9 tan^{2} (x) sec^{3} (x) d x

\frac{4}{x}, 16 x, \frac{1}{16} x

\frac{d}{d x} (- 16 x^{2} + 16 x + 320)

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