What is the integral of-3x^{-3}ln(-4x) ?

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

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integral of-3x^{-3}ln(-4x)

\int - 3 x^{- 3} ln (- 4 x) d x

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

Solution steps

\int - 3 x^{- 3} ln (- 4 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 3 \cdot \int x^{- 3} ln (- 4 x) d x

Apply Integration By Parts

: - \frac{ln ( - 4 x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x

= - 3 (- \frac{ln ( - 4 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}}

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

Add a constant to the solution

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

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