What is the integral of (x+200)^2 ?

The integral of (x+200)^2 is (x^3)/3+200x^2+40000x+C

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integral of (x+200)^2

\int (x + 200)^{2} d x

\frac{x ^{3}}{3} + 200 x^{2} + 40000 x + C

Solution steps

\int (x + 200)^{2} d x

Expand

(x + 200)^{2} : x^{2} + 400 x + 40000

= \int x^{2} + 400 x + 40000 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 400 x d x + \int 40000 d x

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

\int 400 x d x = 200 x^{2}

\int 40000 d x = 40000 x

= \frac{x ^{3}}{3} + 200 x^{2} + 40000 x

Add a constant to the solution

= \frac{x ^{3}}{3} + 200 x^{2} + 40000 x + C

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What is the integral of (x+200)^2 ?
The integral of (x+200)^2 is (x^3)/3+200x^2+40000x+C