Right Screen 2 for II – A3
Example 1:
  x  5x
2
3
 1  dx

Solution:
Step 1: Let u  5 x 2  1
Step 2:
du
 10 x
dx
We chose to let the expression 5 x 2  1 because it is
the expression that is raised to a power not equal to
one.
Took the derivative of both sides of the equation
found in step 1 with respect to x.
Step 3: du  10 x dx
Multiply both sides by dx.
3
 
 
2
Now look at your given problem   x  5 x  1  dx . We know that u  5 x 2  1 so
  u  


substituting this into the given problem yields
3
  x u   dx
Our ultimate goal is setup the problem in terms of u, this means we need to find a correct
substitution for x dx. Using the expression in Step 3, we can do the following:
Step 4:
1
du  x dx
10
Step 5:
  x  5x
2
Divide both sides by 10.
3
1
 1  dx   u 3 du

10
Make all appropriate substitutions.