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

The integral of pi(x+2)^2 is pi((x^3)/3+2x^2+4x)+C

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integral of pi(x+2)^2

\int π (x + 2)^{2} d x

π (\frac{x ^{3}}{3} + 2 x^{2} + 4 x) + C

Solution steps

\int π (x + 2)^{2} d x

Take the constant out:

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

= π \cdot \int (x + 2)^{2} d x

Expand

(x + 2)^{2} : x^{2} + 4 x + 4

= π \cdot \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

= π (\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

= π (\frac{x ^{3}}{3} + 2 x^{2} + 4 x)

Add a constant to the solution

= π (\frac{x ^{3}}{3} + 2 x^{2} + 4 x) + C

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