What is the integral from 1 to 3 of r^3ln(r) ?

The integral from 1 to 3 of r^3ln(r) is -5+81/4 ln(3)

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integral from 1 to 3 of r^3ln(r)

\int_{1}^{3} r^{3} ln (r) d r

- 5 + \frac{81}{4} ln (3)

Decimal

17.24689 \dots

Solution steps

\int_{1}^{3} r^{3} ln (r) d r

Apply Integration By Parts

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

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

= [\frac{1}{4} r^{4} ln (r) - \frac{r ^{4}}{16}]_{1}^{3}

Compute the boundaries:

- 5 + \frac{81}{4} ln (3)

= - 5 + \frac{81}{4} ln (3)

What is the integral from 1 to 3 of r^3ln(r) ?
The integral from 1 to 3 of r^3ln(r) is -5+81/4 ln(3)