Page 212 - ADVANCED MATH F.5

Form Five Form Five

1  1 1  1
(h)  − cos11t − cos5t +  c (i) ln sec x − sec x + 2 sec xc+ 4
2  11 5  4
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3  1 5  2x  1 7  2x  
(j)  − cos   + cos    + c 4 sin x
2  5  3  7  3   (k) e c
− 32 5 2− 1
(l) (m) 0 (n) (sin x − cos )x 6 + c
252 2 6

1 5  1 3  1  
3
x
10. I = − cos sin x + 5  − sin x cos x +  x − sin 2x   + c and
6
6 6  4 8  2  
1 3
I = 7 cos x − 7 cos x + 5 cos x − 3 cos xc+
7 5
 − x   1 3 
11. (a)  2  tan x + 1 x  +  + c (d) 2   3 (x − ) 1 + 2 x − 1 +   c

2 3 2 3
(b) 3 (x + 1) + 2 3 x + 2 c

1 1 1 −  1 
2
8
(e) ln x + 4x +− tan  (x + ) 2 + c

2 2  2 
2 3 π 3
(c) (1 ln x+ ) + 2 c (f)
3 9

1 1 − 11 ln3 1  7 1
−

11. (a) − (b) 22  (c) + ln 2 ln3− (d)
2ln 2 e   6 2
1 4 3ππ−+ 2ln 2 4−
−
14. (a) 5sec − 1 5 x + x − 2 25 + c (b) 6
1 π
(c) (d)
2ln10 4

15. (a) ( sin − 1 ( sin x )) + 1 sin 2sin − 1 ( sin x )) + c
(
1
2
2
4 2
206
Mathematics for Advanced Secondary Schools

30/06/2024 18:02:56
ADVANCED MATH F.5 TG CHAPTERS.indd 206 30/06/2024 18:02:56
ADVANCED MATH F.5 TG CHAPTERS.indd 206