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Popular >

integral of x^2-x+2

Solution

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

Solution

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

Graph

Popular Examples

integral of (4x+3)/(2x^2+3x)ln(2x^2+3x)

\int \frac{4 x + 3}{2 x ^{2} + 3 x} ln (2 x^{2} + 3 x) d x

integral of 1/2 e^{-4x}

\int \frac{1}{2} e^{- 4 x} d x

integral of e^{-1/t}

\int e^{- \frac{1}{t}} d t

integral of (4x)/((x+1)(x-1)^2)

\int \frac{4 x}{( x + 1 ) ( x - 1 ) ^{2}} d x

integral of 4x-12

\int 4 x - 12 d x

Frequently Asked Questions (FAQ)

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