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

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

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integral of (2x-2)^2

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

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

Solution steps

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

Apply Integration By Parts

= (2 x - 2)^{2} x - \int 4 (2 x - 2) x d x

\int 4 (2 x - 2) x d x = 4 (x^{2} (x - 1) - \frac{x ^{3}}{3})

= (2 x - 2)^{2} x - 4 (x^{2} (x - 1) - \frac{x ^{3}}{3})

Simplify

(2 x - 2)^{2} x - 4 (x^{2} (x - 1) - \frac{x ^{3}}{3}) : \frac{4 x ^{3}}{3} - 4 x^{2} + 4 x

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

Add a constant to the solution

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

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