What is the integral from 2 to 7 of t^5ln(t) ?

The integral from 2 to 7 of t^5ln(t) is -13065/4+117649/6 ln(7)-32/3 ln(2)

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integral from 2 to 7 of t^5ln(t)

\int_{2}^{7} t^{5} ln (t) d t

- \frac{13065}{4} + \frac{117649}{6} ln (7) - \frac{32}{3} ln (2)

Decimal

34882.08695 \dots

Solution steps

\int_{2}^{7} t^{5} ln (t) d t

Apply Integration By Parts

: [\frac{1}{6} t^{6} ln (t) - \int \frac{t ^{5}}{6} d t]_{2}^{7}

= [\frac{1}{6} t^{6} ln (t) - \int \frac{t ^{5}}{6} d t]_{2}^{7}

\int \frac{t ^{5}}{6} d t = \frac{t ^{6}}{36}

= [\frac{1}{6} t^{6} ln (t) - \frac{t ^{6}}{36}]_{2}^{7}

Compute the boundaries:

- \frac{13065}{4} + \frac{117649}{6} ln (7) - \frac{32}{3} ln (2)

= - \frac{13065}{4} + \frac{117649}{6} ln (7) - \frac{32}{3} ln (2)

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What is the integral from 2 to 7 of t^5ln(t) ?
The integral from 2 to 7 of t^5ln(t) is -13065/4+117649/6 ln(7)-32/3 ln(2)