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Popular >

integral of (-x+1)^2

Solution

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

Solution

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

Solution steps

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

Expand

(- x + 1)^{2} : x^{2} - 2 x + 1

= \int x^{2} - 2 x + 1 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 2 x d x + \int 1 d x

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

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

\int 1 d x = x

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

Add a constant to the solution

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

Popular Examples

integral of (5x^3-8x^2)

\int (5 x^{3} - 8 x^{2}) d x

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

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

integral of 5x+6

\int 5 x + 6 d x

integral of (x-2)(x+1)

\int (x - 2) (x + 1) d x

integral of 6/(sqrt(2-4x^2))

\int \frac{6}{2 - 4 x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of (-x+1)^2 ?
The integral of (-x+1)^2 is (x^3)/3-x^2+x+C