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Popular >

integral of 2+x-x^2

Solution

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

Solution

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

Solution steps

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

\int 2 d x = 2 x

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

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

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

Add a constant to the solution

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

Popular Examples

integral of ((6x+7))/((x+2)^2)

\int \frac{( 6 x + 7 )}{( x + 2 ) ^{2}} d x

integral of (e^{4x})/(4-e^{4x)}

\int \frac{e ^{4 x}}{4 - e ^{4 x}} d x

integral of 5^{-x}

\int 5^{- x} d x

(\partial)/(\partial x)(y/(x^2(y+3)))

\frac{\partial}{\partial x} (\frac{y}{x ^{2} ( y + 3 )})

(dy)/(dx)=(x+y-1)^3-1

\frac{d y}{d x} = (x + y - 1)^{3} - 1

Frequently Asked Questions (FAQ)

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