What is the integral of (ln(5x))/(x^3) ?

The integral of (ln(5x))/(x^3) is -(ln(5x))/(2x^2)-1/(4x^2)+C

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integral of (ln(5x))/(x^3)

\int \frac{ln ( 5 x )}{x ^{3}} d x

- \frac{ln ( 5 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}} + C

Solution steps

\int \frac{ln ( 5 x )}{x ^{3}} d x

Apply Integration By Parts

: - \frac{ln ( 5 x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x

= - \frac{ln ( 5 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 ( 5 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}}

Add a constant to the solution

= - \frac{ln ( 5 x )}{2 x ^{2}} - \frac{1}{4 x ^{2}} + C

y = 4 x, y = x^{2}

\int_{0}^{1} t d t

h \to 0 lim (5 h + 56)

\frac{d}{d x} (\frac{8}{3 - x})

x \to 0 lim (\frac{e ^{a x} - e ^{b x}}{x})

What is the integral of (ln(5x))/(x^3) ?
The integral of (ln(5x))/(x^3) is -(ln(5x))/(2x^2)-1/(4x^2)+C