What is the integral of ((ln(x^2)))/(x^3) ?

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

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integral of ((ln(x^2)))/(x^3)

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

\frac{ln ( x ^{2} )}{2 x ^{2}} = \frac{ln ( x )}{x ^{2}}

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

Add a constant to the solution

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

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