What is the integral from 1 to 5 of x^4ln(x) ?

The integral from 1 to 5 of x^4ln(x) is 625ln(5)-3124/25

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integral from 1 to 5 of x^4ln(x)

\int_{1}^{5} x^{4} ln (x) d x

625 ln (5) - \frac{3124}{25}

Decimal Notation

880.93869 \dots

Solution steps

\int_{1}^{5} x^{4} ln (x) d x

Apply Integration By Parts

: [\frac{1}{5} x^{5} ln (x) - \int \frac{x ^{4}}{5} d x]_{1}^{5}

= [\frac{1}{5} x^{5} ln (x) - \int \frac{x ^{4}}{5} d x]_{1}^{5}

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

= [\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}]_{1}^{5}

Compute the boundaries:

625 ln (5) - \frac{3124}{25}

= 625 ln (5) - \frac{3124}{25}

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What is the integral from 1 to 5 of x^4ln(x) ?
The integral from 1 to 5 of x^4ln(x) is 625ln(5)-3124/25