What is the integral from 1 to 6 of t^4ln(4t) ?

The integral from 1 to 6 of t^4ln(4t) is -311-2/5 ln(2)+7776/5 ln(24)

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integral from 1 to 6 of t^4ln(4t)

\int_{1}^{6} t^{4} ln (4 t) d t

- 311 - \frac{2}{5} ln (2) + \frac{7776}{5} ln (24)

Decimal

4631.23205 \dots

Solution steps

\int_{1}^{6} t^{4} ln (4 t) d t

Compute the indefinite integral:

\int t^{4} ln (4 t) d t = \frac{1}{5} t^{5} ln (4 t) - \frac{t ^{5}}{25} + C

Compute the boundaries:

\int_{1}^{6} t^{4} ln (4 t) d t = \frac{7776}{5} ln (24) - \frac{7776}{25} - (\frac{2}{5} ln (2) - \frac{1}{25})

= \frac{7776}{5} ln (24) - \frac{7776}{25} - (\frac{2}{5} ln (2) - \frac{1}{25})

Simplify

= - 311 - \frac{2}{5} ln (2) + \frac{7776}{5} ln (24)

What is the integral from 1 to 6 of t^4ln(4t) ?
The integral from 1 to 6 of t^4ln(4t) is -311-2/5 ln(2)+7776/5 ln(24)