The integral of the function 1/x is ln(x), which is a fundamental concept in calculus. To derive this, one can use the relationship between exponential functions and logarithms, particularly focusing on the limit definitions. There is a discussion about the notation for logarithms, with some sources using log[x] to represent the natural logarithm, while others reserve ln[x] for that purpose. The conversation also touches on the differences in notation preferences among mathematicians and engineers, emphasizing that conventions can vary. Understanding these distinctions is important for clarity in mathematical communication.