What is the integral from 2 to 6 of t^2ln(2t) ?

The integral from 2 to 6 of t^2ln(2t) is 72ln(12)-208/9-16/3 ln(2)

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integral from 2 to 6 of t^2ln(2t)

\int_{2}^{6} t^{2} ln (2 t) d t

72 ln (12) - \frac{208}{9} - \frac{16}{3} ln (2)

Decimal

152.10538 \dots

Solution steps

\int_{2}^{6} t^{2} ln (2 t) d t

Apply Integration By Parts

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

\int \frac{t ^{2}}{3} d t = \frac{t ^{3}}{9}

= [\frac{1}{3} t^{3} ln (2 t) - \frac{t ^{3}}{9}]_{2}^{6}

Compute the boundaries:

72 ln (12) - \frac{208}{9} - \frac{16}{3} ln (2)

= 72 ln (12) - \frac{208}{9} - \frac{16}{3} ln (2)

What is the integral from 2 to 6 of t^2ln(2t) ?
The integral from 2 to 6 of t^2ln(2t) is 72ln(12)-208/9-16/3 ln(2)