What is the integral of 6(300+x)^2 ?

The integral of 6(300+x)^2 is 6(90000x+300x^2+(x^3)/3)+C

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integral of 6(300+x)^2

\int 6 (300 + x)^{2} d x

6 (90000 x + 300 x^{2} + \frac{x ^{3}}{3}) + C

Solution steps

\int 6 (300 + x)^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int (300 + x)^{2} d x

Expand

(300 + x)^{2} : 90000 + 600 x + x^{2}

= 6 \cdot \int 90000 + 600 x + 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

= 6 (\int 90000 d x + \int 600 x d x + \int x^{2} d x)

\int 90000 d x = 90000 x

\int 600 x d x = 300 x^{2}

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

= 6 (90000 x + 300 x^{2} + \frac{x ^{3}}{3})

Add a constant to the solution

= 6 (90000 x + 300 x^{2} + \frac{x ^{3}}{3}) + C

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What is the integral of 6(300+x)^2 ?
The integral of 6(300+x)^2 is 6(90000x+300x^2+(x^3)/3)+C