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Popular Calculus >

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

Graph

Popular Examples

derivative of (2x-sqrt(x))(5x+2)

d er i v a t i v e (2 x - x) (5 x + 2)

d/(dt)(sqrt(3t))

\frac{d}{d t} (3 t)

derivative of (x^n/n)

\frac{d}{d x} (\frac{x ^{n}}{n})

limit as x approaches-3 of (x+1)/(x+3)

x \to - 3 lim (\frac{x + 1}{x + 3})

slope of (19,3),(20,3)

s l o p e (19, 3), (20, 3)

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