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

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

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integral of x(x+2)^2

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

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

Solution steps

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

Expand

x (x + 2)^{2} : x^{3} + 4 x^{2} + 4 x

= \int x^{3} + 4 x^{2} + 4 x 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^{3} d x + \int 4 x^{2} d x + \int 4 x d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

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

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

Add a constant to the solution

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

\frac{d}{d x} (x ln (x) + 2 x)

\frac{\partial}{\partial x} (x^{2} ln (x^{2} + y^{2}))

\int (7 x^{6} + 7 x^{3} + 4) d x

\int e^{l n (x^{2})} x d x

\frac{d}{d x} (e^{2 x} - cos (2 x))

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