What is the integral from 2 to 7 of t^4ln(2t) ?

The integral from 2 to 7 of t^4ln(2t) is -671-64/5 ln(2)+16807/5 ln(14)

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integral from 2 to 7 of t^4ln(2t)

\int_{2}^{7} t^{4} ln (2 t) d t

- 671 - \frac{64}{5} ln (2) + \frac{16807}{5} ln (14)

Decimal

8191.05502 \dots

Solution steps

\int_{2}^{7} t^{4} ln (2 t) d t

Compute the indefinite integral:

\int t^{4} ln (2 t) d t = \frac{1}{5} t^{5} ln (2 t) - \frac{t ^{5}}{25} + C

Compute the boundaries:

\int_{2}^{7} t^{4} ln (2 t) d t = \frac{16807}{5} ln (14) - \frac{16807}{25} - (\frac{64}{5} ln (2) - \frac{32}{25})

= \frac{16807}{5} ln (14) - \frac{16807}{25} - (\frac{64}{5} ln (2) - \frac{32}{25})

Simplify

= - 671 - \frac{64}{5} ln (2) + \frac{16807}{5} ln (14)

What is the integral from 2 to 7 of t^4ln(2t) ?
The integral from 2 to 7 of t^4ln(2t) is -671-64/5 ln(2)+16807/5 ln(14)