What is the integral from 0 to 4 of 6xln(x) ?

The integral from 0 to 4 of 6xln(x) is 6(16ln(2)-4)

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integral from 0 to 4 of 6xln(x)

\int_{0}^{4} 6 x ln (x) d x

6 (16 ln (2) - 4)

Decimal

42.54212 \dots

Solution steps

\int_{0}^{4} 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}^{4} x ln (x) d x

Apply Integration By Parts

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

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

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

Compute the boundaries:

16 ln (2) - 4

= 6 (16 ln (2) - 4)

What is the integral from 0 to 4 of 6xln(x) ?
The integral from 0 to 4 of 6xln(x) is 6(16ln(2)-4)