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
Okay, let's integrate (x). This requires integration by parts. Step 1: Set up integration by parts. We use the formula u\,dv = uv - v\,du. Let u = (x) and dv = dx. Step 2: Find du and v. Differentiate u to find du: du = (1)/(x)\,dx Integrate dv to find v: v = dx = x Step 3: Apply the integration by parts formula. Substitute u, v, du, and dv into the formula: (x)\,dx = ((x))(x) - (x)((1)/(x))\,dx Step 4: Simplify and integrate the remaining term. (x)\,dx = x(x) - 1\,dx (x)\,dx = x(x) - x + C The integral of (x)\,dx is x(x) - x + C. That's 2 down. 3 left today — send the next one.