What is the integral from 2 to 4 of x^3ln(x) ?

The integral from 2 to 4 of x^3ln(x) is 124ln(2)-15

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integral from 2 to 4 of x^3ln(x)

\int_{2}^{4} x^{3} ln (x) d x

124 ln (2) - 15

Solution steps

\int_{2}^{4} x^{3} ln (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

124 ln (2) - 15

= 124 ln (2) - 15

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What is the integral from 2 to 4 of x^3ln(x) ?
The integral from 2 to 4 of x^3ln(x) is 124ln(2)-15