What Is The Antiderivative Of 1/x ?

We must find a function f(x) = y such that dy/dx = 1/x .

Firstly, treat dy/dx as a fraction, because it is (it is just a small difference in y over a small difference in x). Raising both sides of the equation to the power of -1 then, we get dx/dy = x => d/dy(x) = x. I.e., x is a function in y such that it is its own derivative. Many will know this to be the exponential function.

Then, x = e^y => log_ex = y. Therefore f(x) = log_ex, also known as the natural logarithm of x, or ln(x).

In conclusion, we have shown that for a function`s derivative to be 1/x, the function must be ln(x) (+c for any constant term that may have been lost during differentiation). I.e., the antiderivative of 1/x is ln(x) (+c).