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

The integral of (2-3x^2)^3 is 8x-12x^3+(54x^5)/5-(27x^7)/7+C

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

integral

(2 - 3 x^{2})^{3}

8 x - 12 x^{3} + \frac{54 x ^{5}}{5} - \frac{27 x ^{7}}{7} + C

Solution steps

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

Expand

(2 - 3 x^{2})^{3} : 8 - 36 x^{2} + 54 x^{4} - 27 x^{6}

= \int 8 - 36 x^{2} + 54 x^{4} - 27 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 8 d x - \int 36 x^{2} d x + \int 54 x^{4} d x - \int 27 x^{6} d x

\int 8 d x = 8 x

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

\int 54 x^{4} d x = \frac{54 x ^{5}}{5}

\int 27 x^{6} d x = \frac{27 x ^{7}}{7}

= 8 x - 12 x^{3} + \frac{54 x ^{5}}{5} - \frac{27 x ^{7}}{7}

Add a constant to the solution

= 8 x - 12 x^{3} + \frac{54 x ^{5}}{5} - \frac{27 x ^{7}}{7} + C

What is the integral of (2-3x^2)^3 ?
The integral of (2-3x^2)^3 is 8x-12x^3+(54x^5)/5-(27x^7)/7+C