What is the integral of ln(x)x^{-3} ?

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

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integral of ln(x)x^{-3}

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

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

Solution steps

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

Simplify

ln (x) x^{- 3} : \frac{ln ( x )}{x ^{3}}

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

Apply Integration By Parts

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

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (x^{2} - 6 y)

(- ln (2 x))^{^{'}}

f (x) = x^{2} + 1, at x = 2

\int 12 - x d x

t \to - 1 lim (1 - 2 t)

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