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

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

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integral of y^3ln(y)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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