What is the integral of-1/7 x^{-8/7} ?

The integral of-1/7 x^{-8/7} is 1/(x^{1/7)}+C

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integral of-1/7 x^{-8/7}

\int - \frac{1}{7} x^{- \frac{8}{7}} d x

\frac{1}{x ^{\frac{1}{7}}} + C

Solution steps

\int - \frac{1}{7} x^{- \frac{8}{7}} d x

Take the constant out:

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

= - \frac{1}{7} \cdot \int x^{- \frac{8}{7}} d x

Apply the Power Rule

: - \frac{7}{x ^{\frac{1}{7}}}

= - \frac{1}{7} (- \frac{7}{x ^{\frac{1}{7}}})

Simplify

- \frac{1}{7} (- \frac{7}{x ^{\frac{1}{7}}}) : \frac{1}{x ^{\frac{1}{7}}}

= \frac{1}{x ^{\frac{1}{7}}}

Add a constant to the solution

= \frac{1}{x ^{\frac{1}{7}}} + C

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What is the integral of-1/7 x^{-8/7} ?
The integral of-1/7 x^{-8/7} is 1/(x^{1/7)}+C