Math 106-01: Calculus II: Reading Homework 7.1

1. Integration by Substition : how is looking for derivatives different from looking for antiderivatives?
   
   1. Method 1 : what is the first method the book suggests? in addition to guessing and checking, what do we need to do with this method?
      
      1. reversing the chain rule : what functions are we looking for when trying to reverse the chain rule?
         
   2. Substitution : how is substitution related to the guess and check method?
      
      1. the method : how does substitution work?
         
      2. why it works : what reservation does the book express regarding the way that dw and dx were treated in the substitution?
         
      3. warning : when does substitution not work?