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
To evaluate the indefinite integral (4x^3 - 6x + 5)\,dx, we will integrate each term separately using the power rule for integration, x^n\,dx = x^n+1n+1 + C, and the constant rule, k\,dx = kx + C. Step 1: Integrate the first term, 4x^3. 4x^3\,dx = 4 x^3\,dx = 4 (x^3+13+1) + C_1 = 4 ((x^4)/(4)) + C_1 = x^4 + C_1 Step 2: Integrate the second term, -6x. -6x\,dx = -6 x^1\,dx = -6 (x^1+11+1) + C_2 = -6 ((x^2)/(2)) + C_2 = -3x^2 + C_2 Step 3: Integrate the third term, 5. 5\,dx = 5x + C_3 Step 4: Combine the results from each term and add a single constant of integration, C, which represents the sum of C_1, C_2, and C_3. (4x^3 - 6x + 5)\,dx = x^4 - 3x^2 + 5x + C The indefinite integral is: x^4 - 3x^2 + 5x + C Last free one today — make it count tomorrow, or type /upgrade for unlimited.