Given dy/dx = 3x2-6x+1, to find y, we need to integrate the expression with respect to x:

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Step 1: Set up the integral. Given dy/dx = 3x²−6x+1, to find y, we need to integrate the expression with respect to x: y = ∫ (3x²−6x+1) dx Step 2: Apply the power rule for integration to each term. The power rule for integration states that ∫ xⁿ dx = (xⁿ⁺¹)/(n+1) + C. ∫ 3x² dx = 3 · (x²⁺¹)/(2+1) = 3 · (x³)/(3) = x³; ∫ −6x dx = −6 · (x¹⁺¹)/(1+1) = −6 · (x²)/(2) = −3x²; ∫ 1 dx = x Step 3: Combine the integrated terms and add the constant of integration. y = x³ − 3x² + x + C; The final answer is y = x³ − 3x² + x + C.

Given (dy)/(dx) = 3x2−6x+1, to find y, we need to integrate the expression with respect to x:

Answer

Step-by-step solution

Set up the integral.

Apply the power rule for integration to each term.

Combine the integrated terms and add the constant of integration.

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