What is the integral from 2 to 5 of t^4ln(2t) ?

The integral from 2 to 5 of t^4ln(2t) is 625ln(10)-3093/25-64/5 ln(2)

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integral from 2 to 5 of t^4ln(2t)

\int_{2}^{5} t^{4} ln (2 t) d t

625 ln (10) - \frac{3093}{25} - \frac{64}{5} ln (2)

Solution steps

\int_{2}^{5} t^{4} ln (2 t) d t

Apply Integration By Parts

: [\frac{1}{5} t^{5} ln (2 t) - \int \frac{t ^{4}}{5} d t]_{2}^{5}

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

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

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

Compute the boundaries:

625 ln (10) - \frac{3093}{25} - \frac{64}{5} ln (2)

= 625 ln (10) - \frac{3093}{25} - \frac{64}{5} ln (2)

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What is the integral from 2 to 5 of t^4ln(2t) ?
The integral from 2 to 5 of t^4ln(2t) is 625ln(10)-3093/25-64/5 ln(2)