What is the integral from 2 to 3 of x^4ln(x) ?

The integral from 2 to 3 of x^4ln(x) is -211/25+(243ln(3)-32ln(2))/5

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integral from 2 to 3 of x^4ln(x)

\int_{2}^{3} x^{4} ln (x) d x

- \frac{211}{25} + \frac{243 ln ( 3 ) - 32 ln ( 2 )}{5}

Decimal

40.51641 \dots

Solution steps

\int_{2}^{3} x^{4} ln (x) d x

Apply Integration By Parts

= [\frac{1}{5} x^{5} ln (x) - \int \frac{x ^{4}}{5} d x]_{2}^{3}

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

= [\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}]_{2}^{3}

Compute the boundaries:

- \frac{211}{25} + \frac{243 ln ( 3 ) - 32 ln ( 2 )}{5}

= - \frac{211}{25} + \frac{243 ln ( 3 ) - 32 ln ( 2 )}{5}

What is the integral from 2 to 3 of x^4ln(x) ?
The integral from 2 to 3 of x^4ln(x) is -211/25+(243ln(3)-32ln(2))/5