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

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

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integral of r^3ln(r)

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

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

Solution steps

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

Apply Integration By Parts

: \frac{1}{4} r^{4} ln (r) - \int \frac{r ^{3}}{4} d r

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

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

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

Add a constant to the solution

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

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