What is the integral from 0 to 3 of 6xln(x) ?

The integral from 0 to 3 of 6xln(x) is 6(9/2 ln(3)-9/4)

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integral from 0 to 3 of 6xln(x)

\int_{0}^{3} 6 x ln (x) d x

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

Decimal Notation

16.16253 \dots

Solution steps

\int_{0}^{3} 6 x ln (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int_{0}^{3} x ln (x) d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{3}

= 6 [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{3}

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

= 6 [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{0}^{3}

Compute the boundaries:

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

= 6 (\frac{9}{2} ln (3) - \frac{9}{4})

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What is the integral from 0 to 3 of 6xln(x) ?
The integral from 0 to 3 of 6xln(x) is 6(9/2 ln(3)-9/4)