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Popular >

integral of-x^2+x+6

Solution

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

Solution

- \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + 6 x + C

Solution steps

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

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

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

\int 6 d x = 6 x

= - \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + 6 x

Add a constant to the solution

= - \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + 6 x + C

Popular Examples

area y=sqrt(x+3),x=-3,y=5 area

y = x + 3, x = - 3, y = 5

(\partial)/(\partial x)(2000e^{(x)(y)})

\frac{\partial}{\partial x} (2000 e^{(x) (y)})

derivative of sqrt(t^2+a^2)derivative of

t^{2} + a^{2}

derivative of x^4e^{10x}

\frac{d}{d x} (x^{4} e^{10 x})

derivative of 8/5 x^{-2/4}

\frac{d}{d x} (\frac{8}{5} x^{- \frac{2}{4}})

Frequently Asked Questions (FAQ)

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