What is the integral of (ln(2x))/(x^4) ?

The integral of (ln(2x))/(x^4) is -(ln(2x))/(3x^3)-1/(9x^3)+C

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integral of (ln(2x))/(x^4)

\int \frac{ln ( 2 x )}{x ^{4}} d x

- \frac{ln ( 2 x )}{3 x ^{3}} - \frac{1}{9 x ^{3}} + C

Solution steps

\int \frac{ln ( 2 x )}{x ^{4}} d x

Apply Integration By Parts

= - \frac{ln ( 2 x )}{3 x ^{3}} - \int - \frac{1}{3 x ^{4}} d x

\int - \frac{1}{3 x ^{4}} d x = \frac{1}{9 x ^{3}}

= - \frac{ln ( 2 x )}{3 x ^{3}} - \frac{1}{9 x ^{3}}

Add a constant to the solution

= - \frac{ln ( 2 x )}{3 x ^{3}} - \frac{1}{9 x ^{3}} + C

What is the integral of (ln(2x))/(x^4) ?
The integral of (ln(2x))/(x^4) is -(ln(2x))/(3x^3)-1/(9x^3)+C