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)

integral

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

- \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

\frac{( x + 2 )}{( x ^{2} + x + 1 )}

\frac{x}{sin ^{2} ( x )}

\frac{x ^{2}}{( 1 + x ) ^{2}}

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

e^{- 5} x

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