What is the integral from 3 to 6 of t^2ln(2t) ?

The integral from 3 to 6 of t^2ln(2t) is 9ln(71663616)-21

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integral from 3 to 6 of t^2ln(2t)

\int_{3}^{6} t^{2} ln (2 t) d t

9 ln (71663616) - 21

Decimal

141.78744 \dots

Solution steps

\int_{3}^{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]_{3}^{6}

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

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

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

Compute the boundaries:

72 ln (12) - 21 - 9 ln (6)

= 72 ln (12) - 21 - 9 ln (6)

Simplify

= 9 ln (71663616) - 21

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What is the integral from 3 to 6 of t^2ln(2t) ?
The integral from 3 to 6 of t^2ln(2t) is 9ln(71663616)-21