What is the integral from 1 to 2 of t^3ln(t) ?

The integral from 1 to 2 of t^3ln(t) is 4ln(2)-15/16

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integral from 1 to 2 of t^3ln(t)

\int_{1}^{2} t^{3} ln (t) d t

4 ln (2) - \frac{15}{16}

Decimal

1.83508 \dots

Solution steps

\int_{1}^{2} t^{3} ln (t) d t

Apply Integration By Parts

= [\frac{1}{4} t^{4} ln (t) - \int \frac{t ^{3}}{4} d t]_{1}^{2}

\int \frac{t ^{3}}{4} d t = \frac{t ^{4}}{16}

= [\frac{1}{4} t^{4} ln (t) - \frac{t ^{4}}{16}]_{1}^{2}

Compute the boundaries:

4 ln (2) - \frac{15}{16}

= 4 ln (2) - \frac{15}{16}

What is the integral from 1 to 2 of t^3ln(t) ?
The integral from 1 to 2 of t^3ln(t) is 4ln(2)-15/16