What is the integral from 0 to 2 of x^4ln(2x) ?

The integral from 0 to 2 of x^4ln(2x) is 64/5 ln(2)-32/25

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integral from 0 to 2 of x^4ln(2x)

\int_{0}^{2} x^{4} ln (2 x) d x

\frac{64}{5} ln (2) - \frac{32}{25}

Decimal

7.59228 \dots

Solution steps

\int_{0}^{2} x^{4} ln (2 x) d x

Apply Integration By Parts

= [\frac{1}{5} x^{5} ln (2 x) - \int \frac{x ^{4}}{5} d x]_{0}^{2}

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

= [\frac{1}{5} x^{5} ln (2 x) - \frac{x ^{5}}{25}]_{0}^{2}

Compute the boundaries:

\frac{64}{5} ln (2) - \frac{32}{25}

= \frac{64}{5} ln (2) - \frac{32}{25}

What is the integral from 0 to 2 of x^4ln(2x) ?
The integral from 0 to 2 of x^4ln(2x) is 64/5 ln(2)-32/25