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

The integral of 2-(x-2)^2 is -(x^3)/3+2x^2-2x+C

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integral of 2-(x-2)^2

integral

2 - (x - 2)^{2}

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

Solution steps

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

\int 2 d x = 2 x

\int (x - 2)^{2} d x = \frac{x ^{3}}{3} - 2 x^{2} + 4 x

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

Simplify

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

Add a constant to the solution

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

e^{- 2} t

\frac{( 2 x ^{2} - 1 )}{( x - x ^{3} )}

\frac{sin ^{2} ( x )}{x}

\frac{3}{x ^{2} - x - 1}

2 t (9 - 4 t^{2})^{\frac{1}{2}}

What is the integral of 2-(x-2)^2 ?
The integral of 2-(x-2)^2 is -(x^3)/3+2x^2-2x+C