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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

(\partial)/(\partial x)((-x^2+3)^2)

\frac{\partial}{\partial x} ((- x^{2} + 3)^{2})

limit as x approaches 0+of (e^{-x}-1)/x

x \to 0 + lim (\frac{e ^{- x} - 1}{x})

limit as x approaches 0+of (x+e^x)^{1/x}

x \to 0 + lim ((x + e^{x})^{\frac{1}{x}})

area y=4x^3,y=100x area

y = 4 x^{3}, y = 100 x

integral of (4x+5)^4

\int (4 x + 5)^{4} d x

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