What is the integral of (-1)/(2sqrt(x)) ?

The integral of (-1)/(2sqrt(x)) is -sqrt(x)+C

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integral of (-1)/(2sqrt(x))

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

- x + C

Solution steps

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

Simplify

= (- \frac{1}{2}) \cdot \int \frac{1}{x} d x

Apply the Power Rule

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

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

Simplify

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

= - x

Add a constant to the solution

= - x + C

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What is the integral of (-1)/(2sqrt(x)) ?
The integral of (-1)/(2sqrt(x)) is -sqrt(x)+C