example22

Solution: This problem is very simple once you realize what to substitute.

Step 1: Substitute u = ln(x) and du = dx:

ò dx = u du

Step 2: Integrate using the Power Rule:

ò u du = u^{(2 + 1)}+ C = u³+ C

Step 3: Plug in the value u represents:

u² + C = (ln(x))² + C.