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
Welcome back — been a while! Let's pick up where you left off. Step 1: Use the power-reducing identity for ^2 x. The identity is ^2 x = (1 - (2x))/(2). Substitute this into the integral: ^2 x \,dx = (1 - (2x))/(2) \,dx Step 2: Separate the integral into two terms. (1 - (2x))/(2) \,dx = (1)/(2) (1 - (2x)) \,dx = (1)/(2) ( 1 \,dx - (2x) \,dx ) Step 3: Integrate each term. The integral of 1 with respect to x is x. For (2x) \,dx, use a substitution u = 2x, so du = 2 \,dx, which means dx = (1)/(2) du. (2x) \,dx = (u) (1)/(2) \,du = (1)/(2) (u) \,du = (1)/(2) (u) + C_1 = (1)/(2) (2x) + C_1 Step 4: Combine the results. (1)/(2) ( x - (1)/(2) (2x) ) + C = (1)/(2)x - (1)/(4)(2x) + C The final answer is (1)/(2)x - (1)/(4)(2x) + C. Send me the next one 📸