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

The integral from 1 to 4 of x^4ln(x) is -1023/25+2048/5 ln(2)

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

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

- \frac{1023}{25} + \frac{2048}{5} ln (2)

Decimal

242.99308 \dots

Solution steps

\int_{1}^{4} 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}^{4}

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

= [\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}]_{1}^{4}

Compute the boundaries:

- \frac{1023}{25} + \frac{2048}{5} ln (2)

= - \frac{1023}{25} + \frac{2048}{5} ln (2)

What is the integral from 1 to 4 of x^4ln(x) ?
The integral from 1 to 4 of x^4ln(x) is -1023/25+2048/5 ln(2)