What is the integral of x^4(2-x^2) ?

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

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integral of x^4(2-x^2)

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

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

arccos (x)

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

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\int - t^{2} + 3 t - 2 d t

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