What is the integral of 4x^{-2}ln(-x) ?

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

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integral of 4x^{-2}ln(-x)

\int 4 x^{- 2} ln (- x) d x

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

Solution steps

\int 4 x^{- 2} ln (- x) d x

Take the constant out:

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

= 4 \cdot \int x^{- 2} ln (- x) d x

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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