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.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).