1. Integration 2

2. What is to be learned?
How to integrate composite functions

3. Fast Tracking
y = (7x + 2)5
let y= u5
where u = 7x + 2
dy/du
= 5u4
du/dx
= 7
dy/dx =
dy/du
du/dx
= 5u4 7
dy/dx
Add 1 to power
=5(7x + 2)4 7

4. Fast Tracking
y = (7x + 2)5
let y= u5
where u = 7x + 2
dy/du
= 5u4
du/dx
= 7
dy/dx =
dy/du
du/dx
÷ 5
= 5u4 7
dy/dx
Add 1 to power
=5(7x + 2)4 7

5. Fast Tracking
y = (7x + 2)5
let y= u5
where u = 7x + 2
dy/du
= 5u4
du/dx
= 7
÷ 7
dy/dx =
dy/du
du/dx
÷ 5
= 5u4 7
dy/dx
Add 1 to power
=5(7x + 2)4 7

6. ∫ ∫ ∫ (ax + b)n (ax + b)n dx Elur Niahc = (ax + b)n+1 a (n+1)5
(4)
= (5x + 7)4
+ c 20

7. ∫ ∫ (9x + 3)6 dx = (9x + 3)7 9 (7) = (9x + 3)7 + c 63 9(5 – 4x)7 dx-4
(8)
= (5 – 4x)8
+ c
-32

8. ∫ ∫ ∫ Integration 2 Elur Niahc (ax + b)n (ax + b)n dx = (ax + b)n+13
(7)
= (3x + 8)7
+ c 21