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

= - \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

f (x) = \frac{( x ^{2} + 9 )}{( x ^{2} - 9 )}

\int_{b}^{2 b} x^{3} d x

6 + x - x^{2}, 4

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

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

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