Integral of 1/x

A student asks, I need to learn about the integral of 1/x.

solution
Let's consider the indefinite integral,
 * $$\int \! {\frac {1} {x}} \,dx \,$$

The solution is $$\log(x)+C$$

Now, let's consider the definite integral,
 * $$\int_a^b \! {\frac {1} {x}} \,dx \,$$

Evaluating the indefinite integral at its limits, we get


 * $$\log(x)+C \: \bigg{|}_a^b = \log(b) - \log(a) $$