What is the integral of x^{11}ln(2x^6) ?

The integral of x^{11}ln(2x^6) is 1/12 x^{12}(ln(2)+6ln(x))-(x^{12})/(24)+C

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integral of x^{11}ln(2x^6)

\int x^{11} ln (2 x^{6}) d x

\frac{1}{12} x^{12} (ln (2) + 6 ln (x)) - \frac{x ^{12}}{24} + C

Solution steps

\int x^{11} ln (2 x^{6}) d x

Apply Integration By Parts

: \frac{1}{12} x^{12} ln (2 x^{6}) - \int \frac{x ^{11}}{2} d x

= \frac{1}{12} x^{12} ln (2 x^{6}) - \int \frac{x ^{11}}{2} d x

\int \frac{x ^{11}}{2} d x = \frac{x ^{12}}{24}

= \frac{1}{12} x^{12} ln (2 x^{6}) - \frac{x ^{12}}{24}

Simplify

ln (2 x^{6}) : 6 ln (x) + ln (2)

= \frac{1}{12} x^{12} (ln (2) + 6 ln (x)) - \frac{x ^{12}}{24}

Add a constant to the solution

= \frac{1}{12} x^{12} (ln (2) + 6 ln (x)) - \frac{x ^{12}}{24} + C

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What is the integral of x^{11}ln(2x^6) ?
The integral of x^{11}ln(2x^6) is 1/12 x^{12}(ln(2)+6ln(x))-(x^{12})/(24)+C