Page 191 - ADVANCED MATH F.5

Form Five Form Five

numerator is divided by the denominator and the fraction is
expressed as a sum of the quotient and proper fraction. Lead
them to intergrate the partial fractions.
3. Instruct students to use Table 9.2 in the Student’s Book to see
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some forms of rational functions, their partial fractions, and
corresponding integrals.

4. Use Examples 9.26 to 9.30 in the Student’s Book to engage
students and assist them in finding solutions of integrals that
involve rational functions. Engage students in groups to use
mathematical software to verify the solutions the integrals in
the given examples. Advise them to share their findings for
more inputs.
5. Require students to attempt Exercise 9.6 in the Student’s Book.
Advise students to submit their work. Check the correctness
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 9.6

(x + 5) 2 s 2 1 1
1. ln + c 4. ln 2 − −+ c
x − 2 (s − 1) s − 1 s

1 1 1
1
2. ln x −+ − ln x + 5 c+
36 6(x + 5) 36
3
(2x + ) 1 2 2
x − 1 1 1  5. ln + + c
x
3. ln 1 − 3 tan −  + c x − 2 2 x−
3
)
( 9 x+ 2 2 

185
Mathematics for Advanced Secondary Schools

30/06/2024 18:02:49
ADVANCED MATH F.5 TG CHAPTERS.indd 185
ADVANCED MATH F.5 TG CHAPTERS.indd 185 30/06/2024 18:02:49