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

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

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integral of (9x^{-5})

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

- \frac{9}{4 x ^{4}} + C

Solution steps

\int 9 x^{- 5} d x

Take the constant out:

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

= 9 \cdot \int x^{- 5} d x

Apply the Power Rule

: - \frac{1}{4 x ^{4}}

= 9 (- \frac{1}{4 x ^{4}})

Simplify

9 (- \frac{1}{4 x ^{4}}) : - \frac{9}{4 x ^{4}}

= - \frac{9}{4 x ^{4}}

Add a constant to the solution

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

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