What is the integral of (9x^{-5}-4x^{-1}) ?

The integral of (9x^{-5}-4x^{-1}) is -9/(4x^4)-4ln|x|+C

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integral of (9x^{-5}-4x^{-1})

\int (9 x^{- 5} - 4 x^{- 1}) d x

- \frac{9}{4 x ^{4}} - 4 ln ∣ x ∣ + C

Solution steps

\int 9 x^{- 5} - 4 x^{- 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 9 x^{- 5} d x - \int 4 x^{- 1} d x

\int 9 x^{- 5} d x = - \frac{9}{4 x ^{4}}

\int 4 x^{- 1} d x = 4 ln ∣ x ∣

= - \frac{9}{4 x ^{4}} - 4 ln ∣ x ∣

Add a constant to the solution

= - \frac{9}{4 x ^{4}} - 4 ln ∣ x ∣ + C

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\int - e

What is the integral of (9x^{-5}-4x^{-1}) ?
The integral of (9x^{-5}-4x^{-1}) is -9/(4x^4)-4ln|x|+C