What is the integral from 0 to 2 of (xln(x)) ?

The integral from 0 to 2 of (xln(x)) is 2ln(2)-1

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integral from 0 to 2 of (xln(x))

\int_{0}^{2} (x ln (x)) d x

2 ln (2) - 1

Decimal Notation

0.38629 \dots

Solution steps

\int_{0}^{2} x ln (x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{2}

= [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{2}

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

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{0}^{2}

Compute the boundaries:

2 ln (2) - 1

= 2 ln (2) - 1

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What is the integral from 0 to 2 of (xln(x)) ?
The integral from 0 to 2 of (xln(x)) is 2ln(2)-1