What is the integral of (2-s)sqrt(s) ?

The integral of (2-s)sqrt(s) is 4/3 s^{3/2}-2/5 s^{5/2}+C

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integral of (2-s)sqrt(s)

\int (2 - s) s d s

\frac{4}{3} s^{\frac{3}{2}} - \frac{2}{5} s^{\frac{5}{2}} + C

Solution steps

\int (2 - s) s d s

Expand

(2 - s) s : 2 s - s^{\frac{3}{2}}

= \int 2 s - s^{\frac{3}{2}} d s

Apply the Sum Rule:

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

= \int 2 s d s - \int s^{\frac{3}{2}} d s

\int 2 s d s = \frac{4}{3} s^{\frac{3}{2}}

\int s^{\frac{3}{2}} d s = \frac{2}{5} s^{\frac{5}{2}}

= \frac{4}{3} s^{\frac{3}{2}} - \frac{2}{5} s^{\frac{5}{2}}

Add a constant to the solution

= \frac{4}{3} s^{\frac{3}{2}} - \frac{2}{5} s^{\frac{5}{2}} + C

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What is the integral of (2-s)sqrt(s) ?
The integral of (2-s)sqrt(s) is 4/3 s^{3/2}-2/5 s^{5/2}+C