What is the integral of sqrt(x^{-7)} ?

The integral of sqrt(x^{-7)} is -2/(5x^{5/2)}+C

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integral of sqrt(x^{-7)}

\int x^{- 7} d x

- \frac{2}{5 x ^{\frac{5}{2}}} + C

Solution steps

\int x^{- 7} d x

x^{- 7} = x^{- \frac{7}{2}},

assuming

x \geq 0

= \int x^{- \frac{7}{2}} d x

Apply the Power Rule

: - \frac{2}{5 x ^{\frac{5}{2}}}

= - \frac{2}{5 x ^{\frac{5}{2}}}

Add a constant to the solution

= - \frac{2}{5 x ^{\frac{5}{2}}} + C

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What is the integral of sqrt(x^{-7)} ?
The integral of sqrt(x^{-7)} is -2/(5x^{5/2)}+C