What is the integral of (ln(4x))/(x^3) ?

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

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integral of (ln(4x))/(x^3)

\int \frac{ln ( 4 x )}{x ^{3}} d x

- \frac{ln ( 4 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}} + C

Solution steps

\int \frac{ln ( 4 x )}{x ^{3}} d x

Apply Integration By Parts

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

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

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

Add a constant to the solution

= - \frac{ln ( 4 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}} + C

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