How do I integrate ln(x)?
The natural logarithm of x, ln(x), can be integrated using the following formula:

∫ ln(x) dx = x ln(x) - x + C, where C is an arbitrary constant of integration.

This can be derived using the substitution method, where u = ln(x), and du/dx = 1/x. The resulting integral will have the form ∫ u du, which is easily solvable using basic integration rules.
well, i don't think it's easy. what do you mean by an arbitrary constant? how do i know what the constant is?
The constant can be any real number. This is because the derivative of any constant is zero, so if d/dx f(x) = g(x), then all functions f(x)+c also have a derivative of g(x). When doing a proper integral, the two constants cancel out due to the fundamental theorem of calculus, which is ∫ from a to b f(x) dx = F(b) - F(a), where F is the antiderivative of f.
Can you give me an example? let's say I want to know the value of the integral between 1 and 3.