What is the integral of x^4(5-x^2) ?

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

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integral of x^4(5-x^2)

\int x^{4} (5 - x^{2}) d x

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

Solution steps

\int x^{4} (5 - x^{2}) d x

Expand

x^{4} (5 - x^{2}) : 5 x^{4} - x^{6}

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

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

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

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

Add a constant to the solution

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

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