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
Fresh day Senior, let's solve. To solve the integral (3x-2)^5 dx, we can use the substitution method. Step 1: Set up the substitution. Let u = 3x - 2. Step 2: Differentiate u with respect to x to find du. (du)/(dx) = (d)/(dx)(3x - 2) = 3 This means du = 3 \, dx. Step 3: Express dx in terms of du. dx = (1)/(3) du Step 4: Substitute u and dx into the original integral. (3x-2)^5 dx = u^5 ((1)/(3) du) = (1)/(3) u^5 du Step 5: Integrate with respect to u using the power rule for integration, u^n du = u^n+1n+1 + C. (1)/(3) u^5 du = (1)/(3) · u^5+15+1 + C = (1)/(3) · (u^6)/(6) + C = (u^6)/(18) + C Step 6: Substitute back u = 3x - 2 to express the answer in terms of x. ((3x-2)^6)/(18) + C The final answer is ((3x-2)^6)/(18) + C. Send me the next one 📸