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 sum/difference rule and constant multiple rule for integration. (2x^3-5x^2+4x-1)\,dx = 2x^3\,dx - 5x^2\,dx + 4x\,dx - 1\,dx = 2 x^3\,dx - 5 x^2\,dx + 4 x\,dx - 1\,dx Step 2: Apply the power rule for integration, x^n\,dx = x^n+1n+1 + C. 2(x^3+13+1) - 5(x^2+12+1) + 4(x^1+11+1) - (x^0+10+1) + C = 2((x^4)/(4)) - 5((x^3)/(3)) + 4((x^2)/(2)) - x + C Step 3: Simplify the expression. = (2x^4)/(4) - (5x^3)/(3) + (4x^2)/(2) - x + C = (1)/(2)x^4 - (5)/(3)x^3 + 2x^2 - x + C The final answer is (1)/(2)x^4 - (5)/(3)x^3 + 2x^2 - x + C. 3 done, 2 left today. You're making progress.