Solution: Step 1: Let u = ln(x) and dv = 1 dx. We find that du = dx and v = ò dv = ò dx = x.

Step 2: Substitute these variables into the formula:

ò ln(x) dx = ò u dv = uv - ò v du = x[ln(x)] - ò dx.

Step 3: Integrate the integral by using the ln(u) Rule:

x[ln(x)] - ò dx = x[ln(x)] - x + C.

Step 4: Check the result:

(x[ln(x)] - x + C) = (1(ln(x)) + - 1 = ln(x).