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Popular Calculus >

integral of x(7-x^2)

Solution

\int x (7 - x^{2}) d x

Solution

\frac{7 x ^{2}}{2} - \frac{x ^{4}}{4} + C

Solution steps

\int x (7 - x^{2}) d x

Expand

x (7 - x^{2}) : 7 x - x^{3}

= \int 7 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 7 x d x - \int x^{3} d x

\int 7 x d x = \frac{7 x ^{2}}{2}

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

= \frac{7 x ^{2}}{2} - \frac{x ^{4}}{4}

Add a constant to the solution

= \frac{7 x ^{2}}{2} - \frac{x ^{4}}{4} + C

Graph

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Frequently Asked Questions (FAQ)

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