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Popular >

integral of (1-x)^2

Solution

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

Solution

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

Solution steps

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

Expand

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

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

\int 1 d x = x

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

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

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

Add a constant to the solution

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

Popular Examples

integral of xsin(5-x)

\int x sin (5 - x) d x

inverse oflaplace 8/s inverse laplace

\frac{8}{s}

y^{''}+y^'-20y=-1200t^3

y^{^{''}} + y^{^{'}} - 20 y = - 1200 t^{3}

(\partial)/(\partial x)((x+y)(xy+1))

\frac{\partial}{\partial x} ((x + y) (x y + 1))

integral of sqrt(x^2+6x+11)

\int x^{2} + 6 x + 11 d x

Frequently Asked Questions (FAQ)

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