What is the integral from 1 to 8 of xln(x) ?

The integral from 1 to 8 of xln(x) is 96ln(2)-63/4

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integral from 1 to 8 of xln(x)

\int_{1}^{8} x ln (x) d x

96 ln (2) - \frac{63}{4}

Decimal

50.79212 \dots

Solution steps

\int_{1}^{8} x ln (x) d x

Apply Integration By Parts

= [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{1}^{8}

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

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{1}^{8}

Compute the boundaries:

96 ln (2) - \frac{63}{4}

= 96 ln (2) - \frac{63}{4}

What is the integral from 1 to 8 of xln(x) ?
The integral from 1 to 8 of xln(x) is 96ln(2)-63/4