What is the integral from 1 to 3 of 3x^4ln(x) ?

The integral from 1 to 3 of 3x^4ln(x) is 3(-242/25+243/5 ln(3))

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integral from 1 to 3 of 3x^4ln(x)

\int_{1}^{3} 3 x^{4} ln (x) d x

3 (- \frac{242}{25} + \frac{243}{5} ln (3))

Decimal Notation

131.13767 \dots

Solution steps

\int_{1}^{3} 3 x^{4} ln (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{1}^{3} 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}^{3}

= 3 [\frac{1}{5} x^{5} ln (x) - \int \frac{x ^{4}}{5} d x]_{1}^{3}

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

= 3 [\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}]_{1}^{3}

Compute the boundaries:

- \frac{242}{25} + \frac{243}{5} ln (3)

= 3 (- \frac{242}{25} + \frac{243}{5} ln (3))

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What is the integral from 1 to 3 of 3x^4ln(x) ?
The integral from 1 to 3 of 3x^4ln(x) is 3(-242/25+243/5 ln(3))