What is the integral from 2 to 4 of 8xln(x) ?

The integral from 2 to 4 of 8xln(x) is 8(14ln(2)-3)

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integral from 2 to 4 of 8xln(x)

\int_{2}^{4} 8 x ln (x) d x

8 (14 ln (2) - 3)

Decimal

53.63248 \dots

Solution steps

\int_{2}^{4} 8 x ln (x) d x

Take the constant out:

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

= 8 \cdot \int_{2}^{4} x ln (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

14 ln (2) - 3

= 8 (14 ln (2) - 3)

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What is the integral from 2 to 4 of 8xln(x) ?
The integral from 2 to 4 of 8xln(x) is 8(14ln(2)-3)