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

The integral from 1 to 3 of x^3ln(x) is -5+81/4 ln(3)

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integral from 1 to 3 of x^3ln(x)

\int_{1}^{3} x^{3} ln (x) d x

- 5 + \frac{81}{4} ln (3)

Decimal Notation

17.24689 \dots

Solution steps

\int_{1}^{3} x^{3} ln (x) d x

Apply Integration By Parts

: [\frac{1}{4} x^{4} ln (x) - \int \frac{x ^{3}}{4} d x]_{1}^{3}

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

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

= [\frac{1}{4} x^{4} ln (x) - \frac{x ^{4}}{16}]_{1}^{3}

Compute the boundaries:

- 5 + \frac{81}{4} ln (3)

= - 5 + \frac{81}{4} ln (3)

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What is the integral from 1 to 3 of x^3ln(x) ?
The integral from 1 to 3 of x^3ln(x) is -5+81/4 ln(3)