What is the integral of 4x^{-1/2} ?

The integral of 4x^{-1/2} is 8x^{1/2}+C

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integral of 4x^{-1/2}

\int 4 x^{- \frac{1}{2}} d x

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

Solution steps

\int 4 x^{- \frac{1}{2}} d x

Take the constant out:

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

= 4 \cdot \int x^{- \frac{1}{2}} d x

Apply the Power Rule

= 4 \cdot 2 x^{\frac{1}{2}}

Simplify

= 8 x^{\frac{1}{2}}

Add a constant to the solution

= 8 x^{\frac{1}{2}} + C

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