Step 1: Understand that we want to find the integral of the function f(x) = 1/x.
Step 2: Recall that the integral is the opposite of the derivative. We are looking for a function whose derivative is 1/x.
Step 3: Remember the natural logarithm function, ln(x). The derivative of ln(x) is 1/x for x > 0.
Step 4: Since we want to include negative values of x as well, we use the absolute value: ln|x|. This ensures the function works for both positive and negative x.
Step 5: Add a constant C to the result. This constant represents any constant value that could be added to the function without changing its derivative.
Step 6: Combine everything to write the final answer: The integral of 1/x is ln|x| + C.
