What is the integral of (-1)/(x^6) ?

The integral of (-1)/(x^6) is 1/(5x^5)+C

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integral of (-1)/(x^6)

\int \frac{- 1}{x ^{6}} d x

\frac{1}{5 x ^{5}} + C

Solution steps

\int \frac{- 1}{x ^{6}} d x

Take the constant out:

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

= - \int \frac{1}{x ^{6}} d x

Apply the Power Rule

: - \frac{1}{5 x ^{5}}

= - (- \frac{1}{5 x ^{5}})

Simplify

= \frac{1}{5 x ^{5}}

Add a constant to the solution

= \frac{1}{5 x ^{5}} + C

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