What is the integral of (3-sqrt(x))^2 ?

The integral of (3-sqrt(x))^2 is 9x-4x^{3/2}+(x^2)/2+C

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integral of (3-sqrt(x))^2

\int (3 - x)^{2} d x

9 x - 4 x^{\frac{3}{2}} + \frac{x ^{2}}{2} + C

Solution steps

\int (3 - x)^{2} d x

Expand

(3 - x)^{2} : 9 - 6 x + x

= \int 9 - 6 x + x d x

Apply the Sum Rule:

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

= \int 9 d x - \int 6 x d x + \int x d x

\int 9 d x = 9 x

\int 6 x d x = 4 x^{\frac{3}{2}}

\int x d x = \frac{x ^{2}}{2}

= 9 x - 4 x^{\frac{3}{2}} + \frac{x ^{2}}{2}

Add a constant to the solution

= 9 x - 4 x^{\frac{3}{2}} + \frac{x ^{2}}{2} + C

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What is the integral of (3-sqrt(x))^2 ?
The integral of (3-sqrt(x))^2 is 9x-4x^{3/2}+(x^2)/2+C