What is the integral of (ln(6x))/(x^8) ?

The integral of (ln(6x))/(x^8) is -(ln(6x))/(7x^7)-1/(49x^7)+C

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integral of (ln(6x))/(x^8)

\int \frac{ln ( 6 x )}{x ^{8}} d x

- \frac{ln ( 6 x )}{7 x ^{7}} - \frac{1}{49 x ^{7}} + C

Solution steps

\int \frac{ln ( 6 x )}{x ^{8}} d x

Apply Integration By Parts

= - \frac{ln ( 6 x )}{7 x ^{7}} - \int - \frac{1}{7 x ^{8}} d x

\int - \frac{1}{7 x ^{8}} d x = \frac{1}{49 x ^{7}}

= - \frac{ln ( 6 x )}{7 x ^{7}} - \frac{1}{49 x ^{7}}

Add a constant to the solution

= - \frac{ln ( 6 x )}{7 x ^{7}} - \frac{1}{49 x ^{7}} + C

What is the integral of (ln(6x))/(x^8) ?
The integral of (ln(6x))/(x^8) is -(ln(6x))/(7x^7)-1/(49x^7)+C