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Popular Calculus >

integral of (2x-2)^3

Solution

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

Solution

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

Graph

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Frequently Asked Questions (FAQ)

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