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

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

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integral of 4/(sqrt(u))

\int \frac{4}{u} d u

8 u + C

Solution steps

\int \frac{4}{u} d u

Take the constant out:

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

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

Apply the Power Rule

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

Simplify

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

= 8 u

Add a constant to the solution

= 8 u + C