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Popular Calculus >

integral of (x-4)^2

Solution

\int (x - 4)^{2} d x

Solution

\frac{x ^{3}}{3} - 4 x^{2} + 16 x + C

Solution steps

\int (x - 4)^{2} d x

Expand

(x - 4)^{2} : x^{2} - 8 x + 16

= \int x^{2} - 8 x + 16 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 8 x d x + \int 16 d x

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

\int 8 x d x = 4 x^{2}

\int 16 d x = 16 x

= \frac{x ^{3}}{3} - 4 x^{2} + 16 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 4 x^{2} + 16 x + C

Graph

Popular Examples

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(dy}{dx}-(7y)/x =\frac{y^3)/(x^9)

derivative of (3x^2/(2x+1))

(dy)/(dx)=((x-2))/((y-2))

Frequently Asked Questions (FAQ)

What is the integral of (x-4)^2 ?
The integral of (x-4)^2 is (x^3)/3-4x^2+16x+C