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

The integral of (2-(x^2)/2)^2 is 4x-(2x^3)/3+(x^5)/(20)+C

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integral of (2-(x^2)/2)^2

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

4 x - \frac{2 x ^{3}}{3} + \frac{x ^{5}}{20} + C

Solution steps

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

Simplify

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

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

\int 4 d x = 4 x

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

\int \frac{x ^{4}}{4} d x = \frac{x ^{5}}{20}

= 4 x - \frac{2 x ^{3}}{3} + \frac{x ^{5}}{20}

Add a constant to the solution

= 4 x - \frac{2 x ^{3}}{3} + \frac{x ^{5}}{20} + C

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What is the integral of (2-(x^2)/2)^2 ?
The integral of (2-(x^2)/2)^2 is 4x-(2x^3)/3+(x^5)/(20)+C