What is the result of ∫ (x^2 - 4x + 4) dx?

To determine the result of the integral ∫ (x^2 - 4x + 4) dx, we first rewrite the integrand in a more familiar form. The expression x^2 - 4x + 4 is a quadratic polynomial that can be factored as (x - 2)^2. However, we can also directly integrate each term of the polynomial without factoring.

When integrating, we apply the power rule for integration, which states that ∫ x^n dx = (1/(n+1)) x^(n+1) + C, where C is the constant of integration.

1. For the term x^2, applying the power rule gives:

∫ x^2 dx = (1/3)x^3.

2. For the term -4x, the integration yields:

∫ -4x dx = -4 * (1/2)x^2 = -2x^2.

3. Finally, for the constant term 4, we have:

∫ 4 dx = 4x.

Combining all these results together, we get:

∫ (x^2 - 4x + 4) dx = (1/3)x