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Popular >

integral of (1-2x)^2

Solution

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

Solution

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

Solution steps

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

Expand

(1 - 2 x)^{2} : 1 - 4 x + 4 x^{2}

= \int 1 - 4 x + 4 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 4 x d x + \int 4 x^{2} d x

\int 1 d x = x

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

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

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

Add a constant to the solution

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

Popular Examples

d/(dθ)(4-sin(θ))

\frac{d}{d θ} (4 - sin (θ))

integral of 1/(sqrt(21-4x-x^2))

\int \frac{1}{21 - 4 x - x ^{2}} d x

laplacetransform xe^x laplace transform

x e^{x}

xy^'+y=-5xy^2,y(1)=3

x y^{^{'}} + y = - 5 x y^{2}, y (1) = 3

y^{''}+2y^'=2t+3

y^{^{''}} + 2 y^{^{'}} = 2 t + 3

Frequently Asked Questions (FAQ)

What is the integral of (1-2x)^2 ?
The integral of (1-2x)^2 is x-2x^2+(4x^3)/3+C