What is the integral of 200+10x+1/3 x^2 ?

The integral of 200+10x+1/3 x^2 is 200x+5x^2+(x^3)/9+C

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integral of 200+10x+1/3 x^2

\int 200 + 10 x + \frac{1}{3} x^{2} d x

200 x + 5 x^{2} + \frac{x ^{3}}{9} + C

Solution steps

\int 200 + 10 x + \frac{1}{3} 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 200 d x + \int 10 x d x + \int \frac{1}{3} x^{2} d x

\int 200 d x = 200 x

\int 10 x d x = 5 x^{2}

\int \frac{1}{3} x^{2} d x = \frac{x ^{3}}{9}

= 200 x + 5 x^{2} + \frac{x ^{3}}{9}

Add a constant to the solution

= 200 x + 5 x^{2} + \frac{x ^{3}}{9} + C

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What is the integral of 200+10x+1/3 x^2 ?
The integral of 200+10x+1/3 x^2 is 200x+5x^2+(x^3)/9+C