What is the integral of x^{15}ln(3x^8) ?

The integral of x^{15}ln(3x^8) is 1/16 x^{16}(ln(3)+8ln(x))-(x^{16})/(32)+C

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integral of x^{15}ln(3x^8)

\int x^{15} ln (3 x^{8}) d x

\frac{1}{16} x^{16} (ln (3) + 8 ln (x)) - \frac{x ^{16}}{32} + C

Solution steps

\int x^{15} ln (3 x^{8}) d x

Apply Integration By Parts

: \frac{1}{16} x^{16} ln (3 x^{8}) - \int \frac{x ^{15}}{2} d x

= \frac{1}{16} x^{16} ln (3 x^{8}) - \int \frac{x ^{15}}{2} d x

\int \frac{x ^{15}}{2} d x = \frac{x ^{16}}{32}

= \frac{1}{16} x^{16} ln (3 x^{8}) - \frac{x ^{16}}{32}

Simplify

ln (3 x^{8}) : 8 ln (x) + ln (3)

= \frac{1}{16} x^{16} (ln (3) + 8 ln (x)) - \frac{x ^{16}}{32}

Add a constant to the solution

= \frac{1}{16} x^{16} (ln (3) + 8 ln (x)) - \frac{x ^{16}}{32} + C

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What is the integral of x^{15}ln(3x^8) ?
The integral of x^{15}ln(3x^8) is 1/16 x^{16}(ln(3)+8ln(x))-(x^{16})/(32)+C