Integration by Substitution

EXAMPLES:

1. 

 

 

Since 2x is the derivative of x² + 1, integrate x² + 1.  This answer can be checked by
finding the derivative of the answer.



The derivative of the inside function is 2x.  Rewrite the integral as


 

2.  



Separate the absolute value function into separate integrals that can be written without absolute
value signs.  Find where the function equals 0.  The inside function will be negative on one side
of this value and positive on the other.


 

3. Use a substitution method to keep functions straight:



Let u = 2x - 1, the inside function.  Then
du = 2 dx and
du/2 = dx
Substitute into the original integral,


Change the u back to a function in x.