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

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

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

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

\frac{1}{x ^{3}} + C

Solution steps

\int - 3 x^{- 4} d x

Take the constant out:

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

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

Apply the Power Rule

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

Simplify

- 3 (- \frac{1}{3 x ^{3}}) : \frac{1}{x ^{3}}

= \frac{1}{x ^{3}}

Add a constant to the solution

= \frac{1}{x ^{3}} + C