What is the integral from 4 to 8 of t^4ln(3t) ?

The integral from 4 to 8 of t^4ln(3t) is -31744/25+(32768ln(24)-1024ln(12))/5

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integral from 4 to 8 of t^4ln(3t)

\int_{4}^{8} t^{4} ln (3 t) d t

- \frac{31744}{25} + \frac{32768 ln ( 24 ) - 1024 ln ( 12 )}{5}

Decimal

19049.02470 \dots

Solution steps

\int_{4}^{8} t^{4} ln (3 t) d t

Apply Integration By Parts

= [\frac{1}{5} t^{5} ln (3 t) - \int \frac{t ^{4}}{5} d t]_{4}^{8}

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

= [\frac{1}{5} t^{5} ln (3 t) - \frac{t ^{5}}{25}]_{4}^{8}

Compute the boundaries:

- \frac{31744}{25} + \frac{32768 ln ( 24 ) - 1024 ln ( 12 )}{5}

= - \frac{31744}{25} + \frac{32768 ln ( 24 ) - 1024 ln ( 12 )}{5}

What is the integral from 4 to 8 of t^4ln(3t) ?
The integral from 4 to 8 of t^4ln(3t) is -31744/25+(32768ln(24)-1024ln(12))/5