Right Screen 4 for II – A3
Example: Find   x(2 x  1)12  dx
Solution:
Step 1: let u  2x 1
Step 2:
du  2 dx
1
du  dx
2
Since we need to find a correct expression to substitute for x dx, and we can’t multiply
the expression in Step 2 by x (because that is the variable that we are integrating with
respect to), we need to manipulate the expression in Step 1.
Step 3:
u 1  2 x
u 1
x
2
1
 u  1  x
2
Now we can make the appropriate substitutions and solve.


12 

Step 4: 
x
(2 x  1) dx
 1 (u 1)
 1 du
u
2
2
1
  (u  1)(u )12  du
4
1
   u13  u12  du
4
1 1
1

  u14  u13   C
4  14
13 
1
1
 u14  u13  C
56
52
1
1
 (2 x  1)14  (2 x  1)13  C
56
52