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

The integral from 0 to 4 of xln(4x) is 32ln(2)-4

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integral from 0 to 4 of xln(4x)

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

32 ln (2) - 4

Decimal

18.18070 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

32 ln (2) - 4

= 32 ln (2) - 4

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What is the integral from 0 to 4 of xln(4x) ?
The integral from 0 to 4 of xln(4x) is 32ln(2)-4