What is the integral from 3 to 6 of x^4ln(2x) ?

The integral from 3 to 6 of x^4ln(2x) is -7533/25+(-243ln(6)+7776ln(12))/5

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integral from 3 to 6 of x^4ln(2x)

\int_{3}^{6} x^{4} ln (2 x) d x

- \frac{7533}{25} + \frac{- 243 ln ( 6 ) + 7776 ln ( 12 )}{5}

Decimal Notation

3476.12731 \dots

Solution steps

\int_{3}^{6} 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]_{3}^{6}

= [\frac{1}{5} x^{5} ln (2 x) - \int \frac{x ^{4}}{5} d x]_{3}^{6}

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

= [\frac{1}{5} x^{5} ln (2 x) - \frac{x ^{5}}{25}]_{3}^{6}

Compute the boundaries:

- \frac{7533}{25} + \frac{- 243 ln ( 6 ) + 7776 ln ( 12 )}{5}

= - \frac{7533}{25} + \frac{- 243 ln ( 6 ) + 7776 ln ( 12 )}{5}

\int_{0}^{1} 1 - r^{2} \cdot r d r

\int_{- 1}^{1} ∣ 5 x - 3 ∣ d x

\int_{\frac{π}{6}}^{\frac{π}{2}} 6 sin (x) d x

\int_{0}^{\frac{π}{12}} x tan^{2} (4 x) d x

\int_{0}^{1} x (x^{2} - 1) d x

What is the integral from 3 to 6 of x^4ln(2x) ?
The integral from 3 to 6 of x^4ln(2x) is -7533/25+(-243ln(6)+7776ln(12))/5