what is the integral 1/x

What is the integral 1/x ?

$$\small{\text{ We substitute : $ x = e^u \qquad \ dx = e^u\ du $ }}\\ \small{\text{ $\int {\frac{1}{x} }\ dx = \int{\frac{1}{e^u} }\cdot e^u \ du = \int{1}\ du = u $ }}\\\\ \small{\text{Back substitute : $\int {\frac{1}{x} }\ dx = u \qquad u = \ln{(x)} $ }}\\ \small{\text{ $\int {\frac{1}{x} }\ dx = \ln{(x)} + c $ }}$$

$$\int\frac{1}{x}dx=ln(x)+c$$

ln is log to the base e and c is a constant.

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