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 solve the integral (2x) dx, we will use a substitution method. Step 1: Set up the substitution. Let u = 2x. Step 2: Find the differential du. Differentiate u with respect to x: (du)/(dx) = (d)/(dx)(2x) = 2 Rearrange to solve for dx: dx = (du)/(2) Step 3: Substitute u and dx into the integral. (u) ((du)/(2)) Step 4: Pull the constant out of the integral. (1)/(2) (u) du Step 5: Integrate (u) with respect to u. The integral of (u) is (u). Remember to add the constant of integration, C. (1)/(2) ((u) + C) Step 6: Substitute back u = 2x. (1)/(2) (2x) + C The final answer is: (1)/(2)(2x) + C What's next?