What is the integral from 1 to 9 of xln(x) ?

The integral from 1 to 9 of xln(x) is 81ln(3)-20

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integral from 1 to 9 of xln(x)

\int_{1}^{9} x ln (x) d x

81 ln (3) - 20

Solution steps

\int_{1}^{9} x ln (x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{1}^{9}

= [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{1}^{9}

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

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{1}^{9}

Compute the boundaries:

81 ln (3) - 20

= 81 ln (3) - 20

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What is the integral from 1 to 9 of xln(x) ?
The integral from 1 to 9 of xln(x) is 81ln(3)-20