Integrate the function f(x) = 3x2 - 4x + 2.

May 9, 2026Mathematics

ScanSolve AI Answer

May 9, 2026

Answer

$x^3 - 2x^2 + 2x + C$

Step 1: Apply the power rule for integration to each term. The power rule states that $\int x^n \,dx = \frac{x^{n+1}}{n+1} + C$ . $\int (3x^2 - 4x + 2) \,dx$ Integrate $3x^2$ : $\int 3x^2 \,dx = 3 \frac{x^{2+1}}{2+1} = 3 \frac{x^3}{3} = x^3$ Integrate $-4x$ : $\int -4x \,dx = -4 \frac{x^{1+1}}{1+1} = -4 \frac{x^2}{2} = -2x^2$ Integrate $2$ : $\int 2 \,dx = 2x$

Step 2: Combine the integrated terms and add the constant of integration. $x^3 - 2x^2 + 2x + C$

The final answer is $\boxed{x^3 - 2x^2 + 2x + C}$ .

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Quick Answer

Apply the power rule for integration to each term. The power rule states that x^n \,dx = x^n+1n+1 + C.

Asked on May 9, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 9, 2026

Step 1: Apply the power rule for integration to each term. The power rule states that x^n \,dx = x^n+1n+1 + C. (3x^2 - 4x + 2) \,dx Integrate 3x^2: 3x^2 \,dx = 3 x^2+12+1 = 3 (x^3)/(3) = x^3 Integrate -4x: -4x \,dx = -4 x^1+11+1 = -4 (x^2)/(2) = -2x^2 Integrate 2: 2 \,dx = 2x Step 2: Combine the integrated terms and add the constant of integration. x^3 - 2x^2 + 2x + C The final answer is x^3 - 2x^2 + 2x + C. That's 2 down. 3 left today — send the next one.