What is the integral from 2 to 3 of xln(x) ?

The integral from 2 to 3 of xln(x) is -2ln(2)-5/4+9/2 ln(3)

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integral from 2 to 3 of xln(x)

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

- 2 ln (2) - \frac{5}{4} + \frac{9}{2} ln (3)

Decimal

2.30746 \dots

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

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

Compute the boundaries:

- 2 ln (2) - \frac{5}{4} + \frac{9}{2} ln (3)

= - 2 ln (2) - \frac{5}{4} + \frac{9}{2} ln (3)

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What is the integral from 2 to 3 of xln(x) ?
The integral from 2 to 3 of xln(x) is -2ln(2)-5/4+9/2 ln(3)