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Popular Calculus >

integral of x(4-x^2)

Solution

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

Solution

2 x^{2} - \frac{x ^{4}}{4} + C

Solution steps

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

Expand

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

= \int 4 x - x^{3} 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 4 x d x - \int x^{3} d x

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

\int x^{3} d x = \frac{x ^{4}}{4}

= 2 x^{2} - \frac{x ^{4}}{4}

Add a constant to the solution

= 2 x^{2} - \frac{x ^{4}}{4} + C

Graph

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Frequently Asked Questions (FAQ)

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