What is the integral of x^{13}ln(6x^7) ?

The integral of x^{13}ln(6x^7) is 1/14 x^{14}(ln(6)+7ln(x))-(x^{14})/(28)+C

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integral of x^{13}ln(6x^7)

\int x^{13} ln (6 x^{7}) d x

\frac{1}{14} x^{14} (ln (6) + 7 ln (x)) - \frac{x ^{14}}{28} + C

Solution steps

\int x^{13} ln (6 x^{7}) d x

Apply Integration By Parts

: \frac{1}{14} x^{14} ln (6 x^{7}) - \int \frac{x ^{13}}{2} d x

= \frac{1}{14} x^{14} ln (6 x^{7}) - \int \frac{x ^{13}}{2} d x

\int \frac{x ^{13}}{2} d x = \frac{x ^{14}}{28}

= \frac{1}{14} x^{14} ln (6 x^{7}) - \frac{x ^{14}}{28}

Simplify

ln (6 x^{7}) : 7 ln (x) + ln (6)

= \frac{1}{14} x^{14} (ln (6) + 7 ln (x)) - \frac{x ^{14}}{28}

Add a constant to the solution

= \frac{1}{14} x^{14} (ln (6) + 7 ln (x)) - \frac{x ^{14}}{28} + C

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What is the integral of x^{13}ln(6x^7) ?
The integral of x^{13}ln(6x^7) is 1/14 x^{14}(ln(6)+7ln(x))-(x^{14})/(28)+C