2. HOW to use Substitution Method
Step 1 : Know the what is u in the function
Step 2 : Differentiate the u
Step 3: Make the dx as a subject
Step 4: Substitute u
Step 5: Integrate in u term
Step 6: Convert the u in x
Step 7: If the question is definite, substitute the limit
suria/pkk2011
3. (ax b)
Integral of
Example:
n
dx
(4 x 7) 4 dx
u 4x 7
du
4
dx
du
(4 x 7) dx u . 4
1
u du
4
4
4
4
du
dx
4
1 u 4 1
c
4 4 1
1 u5
c
4 5
( 4 x 7) 5
c
20
suria/pkk2011
5. LOGARITHM FUNCTION
Example:
Define u:
1
7 x 2 dx
u 7x 2
Differentiate the u:
du
dx
7
Make dx as a subject
dx
du
7
suria/pkk2011
1
1 du
ax b dx u . a
Substitute u :
1
1 du
7 x 2 dx u . 7
1 1
du
7 u
Integrate:
1
ln u c
7
Convert u in x:
1
ln 7 x 2 c
7
6. Define the ‘U’ for TRIGONOMETRY
function
du
sin(ax b)dx sin u.
a
du
cos(ax b)dx cos u.
a
du
2
sec (ax b)dx tan u. a
suria/pkk2011