What is the integral from 1 to 3 of r^4ln(r) ?

The integral from 1 to 3 of r^4ln(r) is -242/25+243/5 ln(3)

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integral from 1 to 3 of r^4ln(r)

\int_{1}^{3} r^{4} ln (r) d r

- \frac{242}{25} + \frac{243}{5} ln (3)

Decimal Notation

43.71255 \dots

Solution steps

\int_{1}^{3} r^{4} ln (r) d r

Apply Integration By Parts

: [\frac{1}{5} r^{5} ln (r) - \int \frac{r ^{4}}{5} d r]_{1}^{3}

= [\frac{1}{5} r^{5} ln (r) - \int \frac{r ^{4}}{5} d r]_{1}^{3}

\int \frac{r ^{4}}{5} d r = \frac{r ^{5}}{25}

= [\frac{1}{5} r^{5} ln (r) - \frac{r ^{5}}{25}]_{1}^{3}

Compute the boundaries:

- \frac{242}{25} + \frac{243}{5} ln (3)

= - \frac{242}{25} + \frac{243}{5} ln (3)

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What is the integral from 1 to 3 of r^4ln(r) ?
The integral from 1 to 3 of r^4ln(r) is -242/25+243/5 ln(3)