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

The integral from 3 to 6 of t^2ln(t) is 9ln(559872)-21

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

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

9 ln (559872) - 21

Decimal

98.11917 \dots

Solution steps

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

Apply Integration By Parts

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

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

Compute the boundaries:

72 ln (6) - 21 - 9 ln (3)

= 72 ln (6) - 21 - 9 ln (3)

Simplify

= 9 ln (559872) - 21

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What is the integral from 3 to 6 of t^2ln(t) ?
The integral from 3 to 6 of t^2ln(t) is 9ln(559872)-21