What is the integral of (ln(9x))/(x^5) ?

The integral of (ln(9x))/(x^5) is -(ln(9x))/(4x^4)-1/(16x^4)+C

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integral of (ln(9x))/(x^5)

\int \frac{ln ( 9 x )}{x ^{5}} d x

- \frac{ln ( 9 x )}{4 x ^{4}} - \frac{1}{16 x ^{4}} + C

Solution steps

\int \frac{ln ( 9 x )}{x ^{5}} d x

Apply Integration By Parts

: - \frac{ln ( 9 x )}{4 x ^{4}} - \int - \frac{1}{4 x ^{5}} d x

= - \frac{ln ( 9 x )}{4 x ^{4}} - \int - \frac{1}{4 x ^{5}} d x

\int - \frac{1}{4 x ^{5}} d x = \frac{1}{16 x ^{4}}

= - \frac{ln ( 9 x )}{4 x ^{4}} - \frac{1}{16 x ^{4}}

Add a constant to the solution

= - \frac{ln ( 9 x )}{4 x ^{4}} - \frac{1}{16 x ^{4}} + C

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What is the integral of (ln(9x))/(x^5) ?
The integral of (ln(9x))/(x^5) is -(ln(9x))/(4x^4)-1/(16x^4)+C