What is the integral from 1 to 5 of xln(x) ?

The integral from 1 to 5 of xln(x) is -6+25/2 ln(5)

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integral from 1 to 5 of xln(x)

\int_{1}^{5} x ln (x) d x

- 6 + \frac{25}{2} ln (5)

Decimal

14.11797 \dots

Solution steps

\int_{1}^{5} x ln (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

- 6 + \frac{25}{2} ln (5)

= - 6 + \frac{25}{2} ln (5)

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What is the integral from 1 to 5 of xln(x) ?
The integral from 1 to 5 of xln(x) is -6+25/2 ln(5)