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

The integral of ((u-2)/(sqrt(u))) is 2/3 u^{3/2}-4sqrt(u)+C

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integral of ((u-2)/(sqrt(u)))

\int (\frac{u - 2}{u}) d u

\frac{2}{3} u^{\frac{3}{2}} - 4 u + C

Solution steps

\int \frac{u - 2}{u} d u

Expand

\frac{u - 2}{u} : u - \frac{2}{u}

= \int u - \frac{2}{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u d u - \int \frac{2}{u} d u

\int u d u = \frac{2}{3} u^{\frac{3}{2}}

\int \frac{2}{u} d u = 4 u

= \frac{2}{3} u^{\frac{3}{2}} - 4 u

Add a constant to the solution

= \frac{2}{3} u^{\frac{3}{2}} - 4 u + C

What is the integral of ((u-2)/(sqrt(u))) ?
The integral of ((u-2)/(sqrt(u))) is 2/3 u^{3/2}-4sqrt(u)+C