Step 1: Identify the integral you need to evaluate, which is ∫ (1/x) dx.
Step 2: Recall the rule for integrating 1/x. The integral of 1/x is a special case.
Step 3: The result of the integral is the natural logarithm of the absolute value of x, written as ln|x|.
Step 4: Since this is an indefinite integral, you need to add a constant of integration, C.
Step 5: Combine the results to write the final answer: ∫ (1/x) dx = ln|x| + C.
Integration of Rational Functions – This concept involves finding the antiderivative of functions that can be expressed as a ratio of polynomials, specifically focusing on the natural logarithm for the function 1/x.
Absolute Value in Logarithms – Understanding the necessity of using absolute values in the logarithmic function when integrating 1/x to account for both positive and negative values of x.
