Page 186 - ADVANCED MATH F.5

Form Five Form Five

integrals in the given examples. Advise students to share their
findings for more inputs.
3. Direct students to attempt Exercise 9.3 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 9.3
1 1 e 34x−
9
1. (6x − ) 9+c 6. − ln 4 3 +tc− 11. − +c
54 3 14
1 5  x 
2. − (12x− ) +c 7. − 2sin (1 3 + x− ) c 12. 10cos−  − 1 +c

2
5  2 
1 − 2 1 e 2x+ 2
3. − (3t − ) 1 +c 8. − ln 5 7 +xc− 13. +c
6 7 2
1 1
4. − 3ln 1 xc− + 9. ln sec(2θ + 1) +c 14. sin(ax b± )+c
2 a
x ln 2x − 1 1
3
5. 12e + c 10. +c 15. ln sec(ax b± ) +c
2 a

Integration by the inspection method

Teaching steps
1. Guide students to discuss the form of integration that requires
the inspection method. Assist students through discussion to
evaluate integrals where the function is a simple polynomial,
trigonometric, logarithmic, or exponential function.
2. Use Examples 9.12 and 9.13 in the student’s Book, to guide
students to find solutions of the integrals by the inspection
method. Engage students to use scientific calculators and

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