What is the integral of 4/(sqrt(x)) ?

The integral of 4/(sqrt(x)) is 8sqrt(x)+C

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integral of 4/(sqrt(x))

\int \frac{4}{x} d x

8 x + C

Solution steps

\int \frac{4}{x} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{x} d x

Apply the Power Rule

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

Simplify

4 \cdot 2 x^{\frac{1}{2}} : 8 x

= 8 x

Add a constant to the solution

= 8 x + C