What is the integral of (ln(2x))/(x^6) ?

The integral of (ln(2x))/(x^6) is -(ln(2x))/(5x^5)-1/(25x^5)+C

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integral of (ln(2x))/(x^6)

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

- \frac{ln ( 2 x )}{5 x ^{5}} - \frac{1}{25 x ^{5}} + C

Solution steps

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

Apply Integration By Parts

: - \frac{ln ( 2 x )}{5 x ^{5}} - \int - \frac{1}{5 x ^{6}} d x

= - \frac{ln ( 2 x )}{5 x ^{5}} - \int - \frac{1}{5 x ^{6}} d x

\int - \frac{1}{5 x ^{6}} d x = \frac{1}{25 x ^{5}}

= - \frac{ln ( 2 x )}{5 x ^{5}} - \frac{1}{25 x ^{5}}

Add a constant to the solution

= - \frac{ln ( 2 x )}{5 x ^{5}} - \frac{1}{25 x ^{5}} + C

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What is the integral of (ln(2x))/(x^6) ?
The integral of (ln(2x))/(x^6) is -(ln(2x))/(5x^5)-1/(25x^5)+C