What is the integral of-1/2 x^{-3/2} ?

The integral of-1/2 x^{-3/2} is 1/(x^{1/2)}+C

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integral of-1/2 x^{-3/2}

\int - \frac{1}{2} x^{- \frac{3}{2}} d x

\frac{1}{x ^{\frac{1}{2}}} + C

Solution steps

\int - \frac{1}{2} x^{- \frac{3}{2}} d x

Take the constant out:

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

= - \frac{1}{2} \cdot \int x^{- \frac{3}{2}} d x

Apply the Power Rule

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

= - \frac{1}{2} (- \frac{2}{x ^{\frac{1}{2}}})

Simplify

- \frac{1}{2} (- \frac{2}{x ^{\frac{1}{2}}}) : \frac{1}{x ^{\frac{1}{2}}}

= \frac{1}{x ^{\frac{1}{2}}}

Add a constant to the solution

= \frac{1}{x ^{\frac{1}{2}}} + C

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What is the integral of-1/2 x^{-3/2} ?
The integral of-1/2 x^{-3/2} is 1/(x^{1/2)}+C