X2 t04 07 quadratic denominators (2013)

Integrating Quadratic Denominators

axaxdx

axdx

xaxadx

xadx

22

22

2

1


axaxdx

axdx

xaxadx

xadx

22

22

2

1

fractions partial viadone


axaxdx

axdx

xaxadx

xadx

22

22

2

1


caxax

a

cxaxa

a

log21

log21


axaxdx

axdx

xaxadx

xadx

22

22

2

1


caxax

a

cxaxa

a

log21

log21

cax

axadx

122 tan13


axaxdx

axdx

xaxadx

xadx

22

22

2

1


caxax

a

cxaxa

a

log21

log21

cax

axadx

122 tan13

cax

xadx

122

sin4


axaxdx

axdx

xaxadx

xadx

22

22

2

1


caxax

a

cxaxa

a

log21

log21

cax

axadx

122 tan13

cax

xadx

122

sin4

caxxax

dx

2222

log5


axaxdx

axdx

xaxadx

xadx

22

22

2

1


caxax

a

cxaxa

a

log21

log21

cax

axadx

122 tan13

cax

xadx

122

sin4

caxxax

dx

2222

log5

cxaxxa

dx

2222

log6

945 e.g. 2 xxdxi

945 e.g. 2 xxdxi

525

2xdx

945 e.g. 2 xxdxi

525

2xdx

cx

cx

52tan5

52tan

515

1

1

945 e.g. 2 xxdxi

525

2xdx

cx

cx

52tan5

52tan

515

1

1

14

232 xx

dxxii

945 e.g. 2 xxdxi

525

2xdx

cx

cx

52tan5

52tan

515

1

1

14

232 xx

dxxii

14

814

4223

22 xxdxdx

xxx

945 e.g. 2 xxdxi

525

2xdx

cx

cx

52tan5

52tan

515

1

1

14

232 xx

dxxii

14

814

4223

22 xxdxdx

xxx

dxxduxxu42

142

945 e.g. 2 xxdxi

525

2xdx

cx

cx

52tan5

52tan

515

1

1

14

232 xx

dxxii

14

814

4223

22 xxdxdx

xxx

dxxduxxu42

142

328

23

221

xdxduu

945 e.g. 2 xxdxi

525

2xdx

cx

cx

52tan5

52tan

515

1

1

14

232 xx

dxxii

14

814

4223

22 xxdxdx

xxx

dxxduxxu42

142

328

23

221

xdxduu

cxxxu 142log8223 22

1

945 e.g. 2 xxdxi

525

2xdx

cx

cx

52tan5

52tan

515

1

1

14

232 xx

dxxii

14

814

4223

22 xxdxdx

xxx

dxxduxxu42

142

328

23

221

xdxduu

cxxxu 142log8223 22

1

cxxxxx 142log8143 22

dx

xxiii2

3

dx

xxiii2

3

dx

xx

xx

33

23

dx

xxiii2

3

dx

xx

xx

33

23

dxxx

x26

3

dx

xxiii2

3

dx

xx

xx

33

23

dxxx

x26

3

22 6

521

612

21

xxdxdx

xxx

dx

xxiii2

3

dx

xx

xx

33

23

dxxx

x26

3

22 6

521

612

21

xxdxdx

xxx

dxxduxxu12

6 2

dx

xxiii2

3

dx

xx

xx

33

23

dxxx

x26

3

22 6

521

612

21

xxdxdx

xxx

dxxduxxu12

6 2

221

21

4252

521

x

dxduu

dx

xxiii2

3

dx

xx

xx

33

23

dxxx

x26

3

22 6

521

612

21

xxdxdx

xxx

dxxduxxu12

6 2

221

21

4252

521

x

dxduu

cx

u

5212

sin252

21 12

1

dx

xxiii2

3

dx

xx

xx

33

23

dxxx

x26

3

22 6

521

612

21

xxdxdx

xxx

dxxduxxu12

6 2

221

21

4252

521

x

dxduu

cx

u

5212

sin252

21 12

1

cxxx

512sin

256 12

Exercise 2F; odd

Exercise 2H; 1, 2, 5, 6, 9, 15, 17 to 20

X2 t04 07 quadratic denominators (2013)

Education

Transcript of X2 t04 07 quadratic denominators (2013)