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

The integral of (x^2-2)^3 is (x^7)/7-(6x^5)/5+4x^3-8x+C

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integral of (x^2-2)^3

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

\frac{x ^{7}}{7} - \frac{6 x ^{5}}{5} + 4 x^{3} - 8 x + C

Solution steps

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

Expand

(x^{2} - 2)^{3} : x^{6} - 6 x^{4} + 12 x^{2} - 8

= \int x^{6} - 6 x^{4} + 12 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 x^{6} d x - \int 6 x^{4} d x + \int 12 x^{2} d x - \int 8 d x

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

\int 6 x^{4} d x = \frac{6 x ^{5}}{5}

\int 12 x^{2} d x = 4 x^{3}

\int 8 d x = 8 x

= \frac{x ^{7}}{7} - \frac{6 x ^{5}}{5} + 4 x^{3} - 8 x

Add a constant to the solution

= \frac{x ^{7}}{7} - \frac{6 x ^{5}}{5} + 4 x^{3} - 8 x + C

What is the integral of (x^2-2)^3 ?
The integral of (x^2-2)^3 is (x^7)/7-(6x^5)/5+4x^3-8x+C