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
Hey online, good to see you again. Step 1: Identify the integral. The integral to evaluate is: (x)/(49-x^2) dx Step 2: Use substitution. Let u = 49 - x^2. Differentiate u with respect to x: (du)/(dx) = -2x Rearrange to express x \, dx in terms of du: du = -2x \, dx x \, dx = -(1)/(2) du Step 3: Substitute into the integral. Substitute u for 49-x^2 and -(1)/(2) du for x \, dx: (1)/(u) (-(1)/(2)) du = -(1)/(2) (1)/(u) du Step 4: Integrate with respect to u. The integral of (1)/(u) is |u|. -(1)/(2) (1)/(u) du = -(1)/(2) |u| + C Step 5: Substitute back u = 49 - x^2. Replace u with 49 - x^2 to get the final answer in terms of x: -(1)/(2) |49 - x^2| + C The evaluated integral is: -(1)/(2) |49 - x^2| + C Send me the next one 📸