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Popular >

integral of (3x-x^2)

Solution

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

Solution

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

Solution steps

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

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

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

= \frac{3 x ^{2}}{2} - \frac{x ^{3}}{3}

Add a constant to the solution

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

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Frequently Asked Questions (FAQ)

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