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

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

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

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

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

Solution steps

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

Expand

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

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

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

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

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

\int 8 d x = 8 x

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

Add a constant to the solution

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

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