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). Step 1: Assume the base of the logarithm. In calculus, (x) can sometimes imply the natural logarithm (x). However, since you just asked for (x), we will assume (x) refers to the common logarithm, base 10, i.e., _10(x). Step 2: Convert to natural logarithm. We use the change of base formula: _10(x) = ((x))/((10)). Step 3: Set up the integral. _10(x)\,dx = ((x))/((10))\,dx Since (10) is a constant, we can factor it out of the integral: _10(x)\,dx = (1)/((10)) (x)\,dx Step 4: Use the result from the integral of (x). From the previous problem, we know that (x)\,dx = x(x) - x + C. Step 5: Substitute and simplify. _10(x)\,dx = (1)/((10)) (x(x) - x) + C We can also express this using _10(x) again: _10(x)\,dx = x_10(x) - (x)/((10)) + C The integral of (x)\,dx (assuming base 10) is x_10(x) - (x)/((10)) + C. 3 done, 2 left today. You're making progress.