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

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

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integral of (x-x^3)^2

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

\frac{x ^{3}}{3} - \frac{2 x ^{5}}{5} + \frac{x ^{7}}{7} + C

Solution steps

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

Expand

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

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

\int x^{2} d x = \frac{x ^{3}}{3}

\int 2 x^{4} d x = \frac{2 x ^{5}}{5}

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

= \frac{x ^{3}}{3} - \frac{2 x ^{5}}{5} + \frac{x ^{7}}{7}

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{2 x ^{5}}{5} + \frac{x ^{7}}{7} + C

y = (6 x^{2} - 12 x + 12) e^{- 8 x}

\frac{d ^{2}}{d x ^{2}} (x^{2} + 1)

2 x^{2} + 3 x - 4

\frac{d}{d x} (ln (π x))

\int \frac{5}{( x + 1 ) ^{2}} d x

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