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Popular >

integral of 6x-x^2

Solution

\int 6 x - x^{2} d x

Solution

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

Solution steps

\int 6 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 6 x d x - \int x^{2} d x

\int 6 x d x = 3 x^{2}

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

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

Add a constant to the solution

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

Popular Examples

derivative of 3x^2-2x-8

\frac{d}{d x} (3 x^{2} - 2 x - 8)

sqrt(y)dx+(x-8)dy=0,y(9)=36

y d x + (x - 8) d y = 0, y (9) = 36

integral of 1/(x(1-sqrt(x))^2)

\int \frac{1}{x ( 1 - x ) ^{2}} d x

(x+1)(dy)/(dx)=-y+10

(x + 1) \frac{d y}{d x} = - y + 10

tangent of y=x^2-6,(-2,-2)tangent of

y = x^{2} - 6, (- 2, - 2)

Frequently Asked Questions (FAQ)

What is the integral of 6x-x^2 ?
The integral of 6x-x^2 is 3x^2-(x^3)/3+C