Startera)

b)

c)

d)

[ ]

( ) kx

dxxdxx

xdxx

kxdxx

kxdxx

++

−=+=+

−=−=−

++=+

+=

∫ ∫

∫

∫

∫

−

6

4)6(4

6

4

2ln123ln123

12

2ln52

5

ln1

2

2

2

1

2

1

Objective:

to use partial fractions to integrate rational functions

Question 1

kx

xdx

xx

kxxxdxx

xxxx

dxxx

+−−=

+−

+−−−=−

−−

−−

−≡

+−

+−

∫

∫

∫

2

3ln

65

1

2ln3ln2

1

3

1

2

1

3

1

65

1

65

1Integrate

2

2

2

Question 2

=

−−

+−=

+−

−

+−

−≡

+−

−−

∫

∫

∫

2

5ln

9

1

145

2

7ln

9

1

2

1

7

1

9

1

)2(9

1

)7(9

1

65

1

145Evaluate

10

82

10

8

10

8

2

10

82

xx

dx

x

xdx

xx

xxxx

xx

dx

Question 3

10ln10

3

5

45ln

2

18ln4ln2

3

43ln1ln2

)3(

4

3

1

1

2

)3(

4

3

1

1

2

)3)(1(

256

935

256

935

256Integrate

5

2

5

22

22

2

23

2

5

223

2

−=

−−

−+−=

+−++−−=

+

++

+−

−

++

++

−−≡

+−−−−≡

−++−−−

−++−−−

∫

∫

xxxdx

xxx

xxxxx

xx

xxx

xx

dxxxx

xx

C4 Textbook

Exercise 6D

Page 301

Question 6

Exercise 6E

Page 305

Questions 2 to 4