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

The integral of [(3-x^2)^3] is 27x-9x^3+(9x^5)/5-(x^7)/7+C

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integral of [(3-x^2)^3]

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

27 x - 9 x^{3} + \frac{9 x ^{5}}{5} - \frac{x ^{7}}{7} + C

Solution steps

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

Expand

(3 - x^{2})^{3} : 27 - 27 x^{2} + 9 x^{4} - x^{6}

= \int 27 - 27 x^{2} + 9 x^{4} - x^{6} 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 27 d x - \int 27 x^{2} d x + \int 9 x^{4} d x - \int x^{6} d x

\int 27 d x = 27 x

\int 27 x^{2} d x = 9 x^{3}

\int 9 x^{4} d x = \frac{9 x ^{5}}{5}

\int x^{6} d x = \frac{x ^{7}}{7}

= 27 x - 9 x^{3} + \frac{9 x ^{5}}{5} - \frac{x ^{7}}{7}

Add a constant to the solution

= 27 x - 9 x^{3} + \frac{9 x ^{5}}{5} - \frac{x ^{7}}{7} + C

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

x \to 2 + lim (2)

\frac{d}{d x} ((3 x + 5)^{7})

\int_{- 1}^{0} (2 x - e^{x}) d x

\frac{d}{d x} (ln (- x^{2} + 6 x))

What is the integral of [(3-x^2)^3] ?
The integral of [(3-x^2)^3] is 27x-9x^3+(9x^5)/5-(x^7)/7+C