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
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, and constants can be pulled out of the integral. (6x^2 - x + 3)\,dx = 6x^2\,dx - x\,dx + 3\,dx Step 2: Apply the power rule for integration, which is x^n\,dx = x^n+1n+1 + C (for n ≠ -1), to each term. For the first term, 6x^2: 6x^2\,dx = 6 · x^2+12+1 = 6 · (x^3)/(3) For the second term, -x (which is -x^1): -x\,dx = - x^1+11+1 = - (x^2)/(2) For the third term, 3 (which is 3x^0): 3\,dx = 3 · x^0+10+1 = 3 · (x^1)/(1) = 3x Step 3: Combine the results from each term and add the constant of integration, C. 6 · (x^3)/(3) - (x^2)/(2) + 3x + C Step 4: Simplify the expression. 2x^3 - (x^2)/(2) + 3x + C The final answer is 2x^3 - (x^2)/(2) + 3x + C. Send me the next one 📸