What is the integral of (9-2x^2)^2 ?

The integral of (9-2x^2)^2 is 81x-12x^3+(4x^5)/5+C

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integral of (9-2x^2)^2

\int (9 - 2 x^{2})^{2} d x

81 x - 12 x^{3} + \frac{4 x ^{5}}{5} + C

Solution steps

\int (9 - 2 x^{2})^{2} d x

Expand

(9 - 2 x^{2})^{2} : 81 - 36 x^{2} + 4 x^{4}

= \int 81 - 36 x^{2} + 4 x^{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 81 d x - \int 36 x^{2} d x + \int 4 x^{4} d x

\int 81 d x = 81 x

\int 36 x^{2} d x = 12 x^{3}

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

= 81 x - 12 x^{3} + \frac{4 x ^{5}}{5}

Add a constant to the solution

= 81 x - 12 x^{3} + \frac{4 x ^{5}}{5} + C

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What is the integral of (9-2x^2)^2 ?
The integral of (9-2x^2)^2 is 81x-12x^3+(4x^5)/5+C