3. Integration Involving
Inverse Trig
sin 1 c
dx x xc
a x
2 2
a
1
OR cos
a
4. Integration Involving
Inverse Trig
sin 1 c
dx x xc
a x
2 2
a
1
OR cos
a
dx 1 1 x
a 2 x 2 a tan a c
5. Integration Involving
Inverse Trig
sin 1 c
dx x xc
a x
2 2
a
1
OR cos
a
dx 1 1 x
a 2 x 2 a tan a c
e.g.
dx
i
4 x2
6. Integration Involving
Inverse Trig
sin 1 c
dx x xc
a x
2 2
a
1
OR cos
a
dx 1 1 x
a 2 x 2 a tan a c
e.g.
dx
i
4 x2
1 x
sin c
2
7. Integration Involving
Inverse Trig
sin 1 c
dx x xc
a x
2 2
a
1
OR cos
a
dx 1 1 x
a 2 x 2 a tan a c
e.g.
dx
i ii
dx
4 x2 9 x2
1 x
sin c
2
8. Integration Involving
Inverse Trig
sin 1 c
dx x xc
a x
2 2
a
1
OR cos
a
dx 1 1 x
a 2 x 2 a tan a c
e.g.
dx
i ii
dx
4 x2 9 x2
1 x 1 1 x
sin c tan c
2 3 3
9. Integration Involving
Inverse Trig
sin 1 c
dx x xc
a x
2 2
a
1
OR cos
a
dx 1 1 x
a 2 x 2 a tan a c
e.g. 1
dx dx
i ii
dx
iii
4 x2 9 x 2
0 2 x2
1 x 1 1 x
sin c tan c
2 3 3
10. Integration Involving
Inverse Trig
sin 1 c
dx x xc
a x
2 2
a
1
OR cos
a
dx 1 1 x
a 2 x 2 a tan a c
e.g. 1
x
sin 1
1
dx dx
i ii
dx
iii
4 x2 9 x 2
0 2 x 2
2 0
1 x 1 1 x
sin c tan c
2 3 3
11. Integration Involving
Inverse Trig
sin 1 c
dx x xc
a x
2 2
a
1
OR cos
a
dx 1 1 x
a 2 x 2 a tan a c
e.g. 1
x
sin 1
1
dx dx
i ii
dx
iii
4 x2 9 x 2
0 2 x 2
2 0
1 1
1 x 1 1 x sin sin 1 0
sin c tan c 2
2 3 3
12. Integration Involving
Inverse Trig
sin 1 c
dx x xc
a x
2 2
a
OR cos
a
1
dx 1 1 x
a 2 x 2 a tan a c
e.g. 1
x
sin 1
1
dx dx
i ii
dx
iii
4 x2 9 x 2
0 2 x 2
2 0
1 1
1 x 1 1 x sin sin 1 0
sin c tan c 2
2 3 3
0
4
4
13. 0
iv Find sin 1 e x and hence evaluate
d ex
dx
log 2 1 e
2x
dx
14. 0
iv Find sin 1 e x and hence evaluate
d ex
dx
log 2 1 e
2x
dx
ex
d
sin 1 e x
dx 1 e 2 x
15. 0
iv Find sin 1 e x and hence evaluate
d ex
dx
log 2 1 e
2x
dx
ex
d
sin 1 e x
dx 1 e 2 x
dx sin e log 2
0
ex
1 x 0
log 2 1 e
2x
16. 0
iv Find sin 1 e x and hence evaluate
d ex
dx
log 2 1 e
2x
dx
ex
d
sin 1 e x
dx 1 e 2 x
dx sin e log 2
0
ex
1 x 0
log 2 1 e
2x
sin 1 e 0 sin 1 e log 2
1 1 1
sin 1 sin
2
2 6
3
17. 0
iv Find sin 1 e x and hence evaluate
d ex
dx
log 2 1 e
2x
dx
ex
d
sin 1 e x v
dx
dx 1 e 2 x 4 9x2
dx sin e log 2
0
ex
1 x 0
log 2 1 e
2x
sin 1 e 0 sin 1 e log 2
1 1 1
sin 1 sin
2
2 6
3
18. 0
iv Find sin 1 e x and hence evaluate
d ex
dx
log 2 1 e
2x
dx
ex
d
sin 1 e x v
dx
dx
dx 1 e 2 x 4 9x 2
4 2
3 x
dx sin e log 2
0
ex
1 x 0
9
log 2 1 e
2x
sin 1 e 0 sin 1 e log 2
1 1 1
sin 1 sin
2
2 6
3
19. 0
iv Find sin 1 e x and hence evaluate
d ex
dx
log 2 1 e
2x
dx
ex
d
sin 1 e x v
dx
dx
dx 1 e 2 x 4 9x 2
4 2
3 x
dx sin e log 2
0
ex
1 x 0
9
log 2 1 e
2x
1 dx
sin 1 e 0 sin 1 e log 2 3 4 2
x
1 1 1
9
sin 1 sin
2
2 6
3
20. 0
iv Find sin 1 e x and hence evaluate
d ex
dx
log 2 1 e
2x
dx
ex
d
sin 1 e x v
dx
dx
dx 1 e 2 x 4 9x 2
4 2
3 x
dx sin e log 2
0
ex
1 x 0
9
log 2 1 e
2x
1 dx
sin 1 e 0 sin 1 e log 2 3 4 2
x
1 1 1
9
sin 1 sin
2 1 1 3 x
sin c
3 2
2 6
3
21. 0
iv Find sin 1 e x and hence evaluate
d ex
dx
log 2 1 e
2x
dx
ex
d
sin 1 e x v
dx
dx
dx 1 e 2 x 4 9x 2
4 2
3 x
dx sin e log 2
0
ex
1 x 0
9
log 2 1 e
2x
1 dx
sin 1 e 0 sin 1 e log 2 3 4 2
x
1 1 1
9
sin 1 sin
2 1 1 3 x
sin c
3 2
2 6
3 Exercise 1E; 2, 3, 4a, 5b, 6 & 7bdf, 9,
12, 13, 16, 17, 20, 22