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

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

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

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

- \frac{ln ( 3 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}} + C

Solution steps

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

Apply Integration By Parts

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

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

Add a constant to the solution

= - \frac{ln ( 3 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}} + C

(0.2) (4.3)

\int 2 x - 3 e^{x} d x

\frac{d}{d x} (2 x^{2} + 5 x + 18)

t \to 0 lim (\frac{8 ^{t} - 5 ^{t}}{t})

\int \frac{y ^{2}}{y + 1} d y

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