What is the integral of (2x+2)^3 ?

The integral of (2x+2)^3 is 2x^4+8x^3+12x^2+8x+C

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integral of (2x+2)^3

\int (2 x + 2)^{3} d x

2 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + C

Solution steps

\int (2 x + 2)^{3} d x

Expand

(2 x + 2)^{3} : 8 x^{3} + 24 x^{2} + 24 x + 8

= \int 8 x^{3} + 24 x^{2} + 24 x + 8 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 8 x^{3} d x + \int 24 x^{2} d x + \int 24 x d x + \int 8 d x

\int 8 x^{3} d x = 2 x^{4}

\int 24 x^{2} d x = 8 x^{3}

\int 24 x d x = 12 x^{2}

\int 8 d x = 8 x

= 2 x^{4} + 8 x^{3} + 12 x^{2} + 8 x

Add a constant to the solution

= 2 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + C

\frac{2}{( s ^{2} - 2 s + 9 )}

\frac{d}{d x} (- 5 x^{\frac{1}{3}})

\frac{d}{d t} (e^{t} (sin (t) + cos (t)))

y^{^{'''}} + 5 y^{^{''}} - 8 y^{^{'}} - 48 y = 0

\int e - x cos (2 x) d x

What is the integral of (2x+2)^3 ?
The integral of (2x+2)^3 is 2x^4+8x^3+12x^2+8x+C