1. C4 Integration

2. Part 1 – Integrating more complicated functions
C4 Integration
Part 1 – Integrating more complicated functions

3. Integrating Standard Functions

5. Ex 6A page 83

6. Reversing the chain rule – integration by recognition
This works for functions of the form f(ax + b)
For example; integrate w.r.t.x cos(4x - 1)
Start by thinking what would y = sin (4x - 1) differentiate into?
4cos(4x - 1)
So ∫cos(4x – 1) = ¼ sin(4x – 1) + C

7. Reversing the chain rule – integration by recognition
Example 2
For example; integrate w.r.t.x (3x + 4)3
Start by thinking what would y = (3x + 4)4 differentiate into?
4 x 3(3x + 4)3
So ∫ (3x + 4)3 = 1/12 (3x + 4)4 + C

8. Reversing the chain rule – integration by recognition
Example 3
For example; integrate w.r.t.x e2x+3
Start by thinking what would y = e2x+3 differentiate into?
2 e2x+3
So ∫ e2x+3 = ½ e2x+3 + C

9. Reversing the chain rule – integration by recognition
Example 4
For example; integrate w.r.t.x sec4xtan4x
Start by thinking what would y = tan 4x differentiate into? What about y = sec 4x
sec 4x differentiates to 4sec4xtan4x
So ∫ sec 4x tan 4x = ¼ sec 4x + C

10. Ex 6B page 86

11. Using trig identites in integration
From C2?
sin2x + cos2x = 1
Divide by cos2x
tan2x + 1 = sec2x