What is the integral from 1 to 3 of x^5ln(x) ?

The integral from 1 to 3 of x^5ln(x) is -182/9+243/2 ln(3)

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integral from 1 to 3 of x^5ln(x)

\int_{1}^{3} x^{5} ln (x) d x

- \frac{182}{9} + \frac{243}{2} ln (3)

Decimal

113.25917 \dots

Solution steps

\int_{1}^{3} x^{5} ln (x) d x

Apply Integration By Parts

: [\frac{1}{6} x^{6} ln (x) - \int \frac{x ^{5}}{6} d x]_{1}^{3}

= [\frac{1}{6} x^{6} ln (x) - \int \frac{x ^{5}}{6} d x]_{1}^{3}

\int \frac{x ^{5}}{6} d x = \frac{x ^{6}}{36}

= [\frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36}]_{1}^{3}

Compute the boundaries:

- \frac{182}{9} + \frac{243}{2} ln (3)

= - \frac{182}{9} + \frac{243}{2} ln (3)

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What is the integral from 1 to 3 of x^5ln(x) ?
The integral from 1 to 3 of x^5ln(x) is -182/9+243/2 ln(3)