What is the integral from 1 to 6 of x^5ln(x) ?

The integral from 1 to 6 of x^5ln(x) is 7776ln(6)-46655/36

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integral from 1 to 6 of x^5ln(x)

\int_{1}^{6} x^{5} ln (x) d x

7776 ln (6) - \frac{46655}{36}

Decimal Notation

12636.74941 \dots

Solution steps

\int_{1}^{6} 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}^{6}

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

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

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

Compute the boundaries:

7776 ln (6) - \frac{46655}{36}

= 7776 ln (6) - \frac{46655}{36}

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What is the integral from 1 to 6 of x^5ln(x) ?
The integral from 1 to 6 of x^5ln(x) is 7776ln(6)-46655/36