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Form Five Form Five
2
(b) 2e x− 2 + c (c) − + c
3 ln3
x
1 1 1 1 x
1
2
2
5
(d) ln x + 2x ++ c (e) ln x ++ tan − + c
FOR ONLINE READING ONLY
2 2 2 2
x 2
(f) ++ 2ln x + 2 + ln x − + c
3
x
2
1
2
1 tan xc
(g) ln x −+ 1 − 1 ln x + + − 1 +
x − 1 2
1 1 sin − 1 x + 3 + c
(h) tan ( )x − − 1 + c (i)
2
2(x + 1) 2 4
2
(j) 1 ln x+ − ln 1 ln x+ + c (k) − 3(x + 1) + c
3
1 3 1 3 1
2x
(l) ( x + ) 1 2 + ( x − ) 1 2 + c (m) 7 + c
3 3 2ln 7
θ
13 11 1 1
16. (a) ln3+ π (b) ln θ 2 + 16 + 8tan − + c
10 20 2
4
1
(c) ln sec4 + θ tan 4 + θ c
4
x
tan − 1+ 2
3 1
2
(d) ln cos x + sin x + x + 4 2 ln + c
2 2
x
tan − 1+ 2
2
35 128
17. (a) π (b)
256 315
1328 3 17 3
19. (a) (b) + ln3
2835 36 32
1
21. (b) 22. ln(1+ 2)units
3
23. (a) 1 squareunit (b) (eπ− 1) cubic units
207
Mathematics for Advanced Secondary Schools
30/06/2024 18:02:56
ADVANCED MATH F.5 TG CHAPTERS.indd 207 30/06/2024 18:02:56
ADVANCED MATH F.5 TG CHAPTERS.indd 207