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 Answer
let's integrate this expression. The problem asks to evaluate the indefinite integral: (6x^2 - x + 3) \,dx Step 1: Apply the linearity property of integration, which states that the integral of a sum or difference is the sum or difference of the integrals. 6x^2 \,dx - x \,dx + 3 \,dx Step 2: Integrate each term using the power rule for integration, x^n \,dx = x^n+1n+1 + C, and the rule for integrating a constant, k \,dx = kx + C. For the first term, 6x^2 \,dx: 6 · x^2+12+1 = 6 · (x^3)/(3) = 2x^3 For the second term, x \,dx (which is x^1 \,dx): x^1+11+1 = (x^2)/(2) For the third term, 3 \,dx: 3x Step 3: Combine the results of each integral and add the constant of integration, C, since it's an indefinite integral. 2x^3 - (x^2)/(2) + 3x + C The final answer is 2x^3 - (x^2)/(2) + 3x + C. Drop the next question! 📸