Suppose you have the task of finding the antiderivative:

∫[3sin(4x + 2)dx]

You can transform this problem into an easier problem by following a three step process.

It starts with a formula:

u = 4x + 2

Step 1. Find the derivative of u. Write it in the form du = u' dx . Be sure to include the differential when you type in your answer.

Step 2. Solve for dx. Your answer will include the other differential.

Step 3. Substitute. There are two obvious moves

• Replace dx with your answer from Step 2.
• Replace (4x + 2) with u.

Step 4. Find the new antiderivative. Write your answer as a formula involving u. Include + C.

Step 5. In your answer for Step 4, replace u with 4x + 2.