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Popular >

integral of (-x+2)^2

Solution

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

Solution

\frac{x ^{3}}{3} - 2 x^{2} + 4 x + C

Solution steps

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

Expand

(- x + 2)^{2} : x^{2} - 4 x + 4

= \int x^{2} - 4 x + 4 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 4 x d x + \int 4 d x

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

\int 4 x d x = 2 x^{2}

\int 4 d x = 4 x

= \frac{x ^{3}}{3} - 2 x^{2} + 4 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 2 x^{2} + 4 x + C

Popular Examples

integral of 2(x-1)^2

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

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\int cos (\frac{2 y}{x}) d x

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\int 3 x^{2} - cos (x) + c d x

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

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

integral of cos^6(y)sin^3(y)

\int cos^{6} (y) sin^{3} (y) d y

Frequently Asked Questions (FAQ)

What is the integral of (-x+2)^2 ?
The integral of (-x+2)^2 is (x^3)/3-2x^2+4x+C