What is the integral from 2 to 6 of t^5ln(t) ?

The integral from 2 to 6 of t^5ln(t) is 7776ln(6)-11648/9-32/3 ln(2)

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integral from 2 to 6 of t^5ln(t)

\int_{2}^{6} t^{5} ln (t) d t

7776 ln (6) - \frac{11648}{9} - \frac{32}{3} ln (2)

Decimal

12631.10584 \dots

Solution steps

\int_{2}^{6} 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}^{6}

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

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

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

Compute the boundaries:

7776 ln (6) - \frac{11648}{9} - \frac{32}{3} ln (2)

= 7776 ln (6) - \frac{11648}{9} - \frac{32}{3} ln (2)

\int_{0}^{4} - x^{2} + 4 d x

\int_{1}^{4} \frac{2 - t}{t ^{2}} d t

\int_{0}^{2} (x^{2} + 2 x + 1) d x

\int_{0}^{5} 2 t + 2 d t

\int_{0}^{1} \frac{x}{2 - x ^{2}} d x

What is the integral from 2 to 6 of t^5ln(t) ?
The integral from 2 to 6 of t^5ln(t) is 7776ln(6)-11648/9-32/3 ln(2)