What is the integral of 4x^{-5}+6x^{-1}-1 ?

The integral of 4x^{-5}+6x^{-1}-1 is -1/(x^4)+6ln|x|-x+C

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integral of 4x^{-5}+6x^{-1}-1

\int 4 x^{- 5} + 6 x^{- 1} - 1 d x

- \frac{1}{x ^{4}} + 6 ln ∣ x ∣ - x + C

Solution steps

\int 4 x^{- 5} + 6 x^{- 1} - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 x^{- 5} d x + \int 6 x^{- 1} d x - \int 1 d x

\int 4 x^{- 5} d x = - \frac{1}{x ^{4}}

\int 6 x^{- 1} d x = 6 ln ∣ x ∣

\int 1 d x = x

= - \frac{1}{x ^{4}} + 6 ln ∣ x ∣ - x

Add a constant to the solution

= - \frac{1}{x ^{4}} + 6 ln ∣ x ∣ - x + C

What is the integral of 4x^{-5}+6x^{-1}-1 ?
The integral of 4x^{-5}+6x^{-1}-1 is -1/(x^4)+6ln|x|-x+C