Simple Substitution: Animated Example

In this example we use the differential method for finishing the substitution. This is the method usually taught. Don't let the fancy word throw you. If you know how to take a derivative, you also know how to take a differential. In the main text we've already been doing it without calling it "taking the differential." Each time we took the derivative of a subsitution equation and multiplied through by dx, we were taking the differential. For example, a substitution equation might be:

   u  =  sin(x)

Taking the derivative you have:

   du
       =  cos(x)
   dx

When you multiply through by dx you have the differential equivalent of that derivative:

   du  =  cos(x) dx

In the differential method, you simply do the taking of the derivative and the multiplying through by dx all in one step. It's that easy.

Now here's the animated example of integration by simple substitution.

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