ACOW INDEFINITE INTEGRALS MODULE
Updated 5/28/2016
Page 1 of 2
Activity A3- Integration Using Substitution
Integration by substitution allows us to recover functions that required the chain rule to
take their derivatives. When using integration by substitution there are numerous critical
steps in setting up and rewriting the problem. An example(RS2) may help make this
more clear.
The general forms of problems that require substitution(RS3) amy help in recognizing
when to use substitution and what expression to set equal to u.
In the following problems, which expression should you set u equal to?
10
1.   24 x 2  4 x  3x 4  x 2  1 dx
u=


2.
 3x1/ 2  2e x 
   x3/ 2  e x   dx


u=
3.
e x
  x

u=
4.
  x

2

 dx



2
4
x    3 x3  2 x  4 x  dx
3
3

Solve the following.
10
5.   24 x 2  4 x  3x 4  x 2  1 dx


6.
 3x1/ 2  2e x 
   x3/ 2  e x   dx


e x 
dx
7.  
 x 


8.

  x
2


2
4
x    3 x3  2 x  4 x  dx
3
3

u=
ACOW INDEFINITE INTEGRALS MODULE
Updated 5/28/2016
Page 2 of 2
Sometimes we need to manipulate the expression we set equal to u so we can make the
appropriate substitutions. Lets look at this case via an example(RS4).
Solve the following.
9.
  x  4x  5
10.
   x
13
2
 dx

x  1 dx