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

The integral of x^{-3}sqrt(x) is -2/(3x^{3/2)}+C

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

\int x^{- 3} x d x

- \frac{2}{3 x ^{\frac{3}{2}}} + C

Solution steps

\int x^{- 3} x d x

Simplify

x^{- 3} x : \frac{1}{x ^{\frac{5}{2}}}

= \int \frac{1}{x ^{\frac{5}{2}}} d x

Apply the Power Rule

: - \frac{2}{3 x ^{\frac{3}{2}}}

= - \frac{2}{3 x ^{\frac{3}{2}}}

Add a constant to the solution

= - \frac{2}{3 x ^{\frac{3}{2}}} + C

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What is the integral of x^{-3}sqrt(x) ?
The integral of x^{-3}sqrt(x) is -2/(3x^{3/2)}+C