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

= - \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

x \to 1 lim (csc (\frac{x}{2}))

\int \frac{- x}{1 + x ^{2}} d x

n = 1 \sum \infty \frac{1}{n + 10}

\int \frac{0.4}{1 - x ^{2}} d x

\int - x sin (x) d x

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