What is the integral of x^5log_{e}(x) ?

The integral of x^5log_{e}(x) is 1/6 x^6ln(x)-(x^6)/(36)+C

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integral of x^5log_{e}(x)

\int x^{5} lo g_{e} (x) d x

\frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36} + C

Solution steps

\int x^{5} lo g_{e} (x) d x

Simplify

lo g_{e} (x) : ln (x)

= \int x^{5} ln (x) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

= \frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36} + C

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What is the integral of x^5log_{e}(x) ?
The integral of x^5log_{e}(x) is 1/6 x^6ln(x)-(x^6)/(36)+C