Page 187 - ADVANCED MATH F.5

Form Five Form Five

mathematical softwares to verify solutions of the given
integrals in the given examples.
3. Require students to attempt Exercise 9.4 in the student’s Book.
Advise them to submit their work. Check the correctness
FOR ONLINE READING ONLY
of their answers, and provide them constructive feedback.
Encourage students to explore additional resources, such as
online tutorials, Symbolab, Mathematica, or reference books,
to enrich their understanding and for further practice.

Answers to Exercise 9.4

1 2 1 2
1. ( x + 3 x − 2 ) 3 + c 12.  ln ( x + 2  ) + c
2 4  
1 2 2 3
2. − (1 e+ t − ) + c 13. ln 1 x+ 2 + c
2 3
4 2
3. ( 3t − 3 ) 1 + c 14. x − 2 x + 2ln x + 1 3 c− +
9

4. ln 1 e+ x + c 15. 1 ( x − 2 ) 1 3 2 + c
3
5. ln ln x + ln x + c 16. 1 e x + 4x + c
2
1 1 2
6. − sin θ 2 + c or cos θ 2 + c 1 2
2 2 17. sin(3e x ) c+
6
7. − ln cos x − sin x + c t
18. t − 2ln 1 e+ + c
8. x 3 + 6 x + 5 2 c 1
2 5 19. − x ln x + c

9. ln cos + θ sinθ + c 1
1 2 20. − ln x + c
10. ln x +   ln x   + c
2 21. e tan − 1 x + c

11. ln 3 4x+ + 9x − 2 6x + 3 c 22. ln tan(x + 1) + c

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Mathematics for Advanced Secondary Schools

30/06/2024 18:02:48
ADVANCED MATH F.5 TG CHAPTERS.indd 181
ADVANCED MATH F.5 TG CHAPTERS.indd 181 30/06/2024 18:02:48