X2 t04 06 partial fractions (2013)
48
Integration By Partial Fractions dx x P x A find; To
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Transcript of X2 t04 06 partial fractions (2013)
Integration By Partial Fractions
dxxPxA find; To
Integration By Partial Fractions
dxxPxA find; To
divisionaperform,degdegIf1 xPxA
Integration By Partial Fractions
dxxPxA find; To
divisionaperform,degdegIf1 xPxA
xPxPxA factorise,degdegIf2
Integration By Partial Fractions
dxxPxA find; To
divisionaperform,degdegIf1 xPxA
xPxPxA factorise,degdegIf2
ax
Aax
write,factor linear for a)
Integration By Partial Fractions
dxxPxA find; To
divisionaperform,degdegIf1 xPxA
xPxPxA factorise,degdegIf2
ax
Aax
write,factor linear for a)
naxC
axB
axA
ax
2
n
write, factorslinear multiplefor b)
Integration By Partial Fractions
dxxPxA find; To
divisionaperform,degdegIf1 xPxA
xPxPxA factorise,degdegIf2
ax
Aax
write,factor linear for a)
naxC
axB
axA
ax
2
n
write, factorslinear multiplefor b)
cbxaxBAx cbxax
2
2 write, e.g. factors polynomialfor c)
dx
xxi
1 e.g.
2
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
0 x
1
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
0 x
1
1 x
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
0 x
1
1 x1
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
dx
xx
111
0 x
1
1 x1
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
dx
xx
111
cxxx 1log21 2
0 x
1
1 x1
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
dx
xx
111
cxxx 1log21 2
xxdxii 2
3
0 x
1
1 x1
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
dx
xx
111
cxxx 1log21 2
xxdxii 2
3
13xxdx
0 x
1
1 x1
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
dx
xx
111
cxxx 1log21 2
xxdxii 2
3
13xxdx
0 x
1
1 x1
13
1
xxxB
xA
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
dx
xx
111
cxxx 1log21 2
xxdxii 2
3
13xxdx
0 x
1
1 x1
13
1
xxxB
xA
31 BxxA
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
dx
xx
111
cxxx 1log21 2
xxdxii 2
3
13xxdx
0 x
1
1 x1
13
1
xxxB
xA
31 BxxA
330
AAx
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
dx
xx
111
cxxx 1log21 2
xxdxii 2
3
13xxdx
0 x
1
1 x1
13
1
xxxB
xA
31 BxxA
330
AAx
31
Bx
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
dx
xx
111
cxxx 1log21 2
xxdxii 2
3
13xxdx
dx
xx 133
0 x
1
1 x1
13
1
xxxB
xA
31 BxxA
330
AAx
31
Bx
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
dx
xx
111
cxxx 1log21 2
xxdxii 2
3
13xxdx
dx
xx 133
cxx 1log3log3
0 x
1
1 x1
13
1
xxxB
xA
31 BxxA
330
AAx
31
Bx
dx
xxi
1 e.g.
2
xxxxx
2
2 001x
dx
xx
111
cxxx 1log21 2
xxdxii 2
3
13xxdx
dx
xx 133
cxx 1log3log3
0 x
1
1 x1
13
1
xxxB
xA
31 BxxA
330
AAx
31
Bx
cx
x
1log3
dxxx
xiii103
52
dxxx
xiii103
52
dxxx
x25
5
dxxx
xiii103
52
dxxx
x25
5
55225
525
xxBxA
xxx
xB
xA
dxxx
xiii103
52
dxxx
x25
5
55225
525
xxBxA
xxx
xB
xA
73
372
B
Bx
dxxx
xiii103
52
dxxx
x25
5
55225
525
xxBxA
xxx
xB
xA
73
372
B
Bx
7101075
A
Ax
dxxx
xiii103
52
dxxx
x25
5
55225
525
xxBxA
xxx
xB
xA
73
372
B
Bx
7101075
A
Ax
dx
xx 273
5710
dxxx
xiii103
52
dxxx
x25
5
55225
525
xxBxA
xxx
xB
xA
73
372
B
Bx
7101075
A
Ax
dx
xx 273
5710
cxx 2log735log
710
dxxx
xiii103
52
dxxx
x25
5
55225
525
xxBxA
xxx
xB
xA
73
372
B
Bx
7101075
A
Ax
dx
xx 273
5710
cxx 2log735log
710
xxdxiv 3
dxxx
xiii103
52
dxxx
x25
5
55225
525
xxBxA
xxx
xB
xA
73
372
B
Bx
7101075
A
Ax
dx
xx 273
5710
cxx 2log735log
710
xxdxiv 3
12xxdx
dxxx
xiii103
52
dxxx
x25
5
55225
525
xxBxA
xxx
xB
xA
73
372
B
Bx
7101075
A
Ax
dx
xx 273
5710
cxx 2log735log
710
xxdxiv 3
12xxdx
11
11
12
22
xCBxxAxxx
CBxxA
dxxx
xiii103
52
dxxx
x25
5
55225
525
xxBxA
xxx
xB
xA
73
372
B
Bx
7101075
A
Ax
dx
xx 273
5710
cxx 2log735log
710
xxdxiv 3
12xxdx
11
11
12
22
xCBxxAxxx
CBxxA
10
Ax
dxxx
xiii103
52
dxxx
x25
5
55225
525
xxBxA
xxx
xB
xA
73
372
B
Bx
7101075
A
Ax
dx
xx 273
5710
cxx 2log735log
710
xxdxiv 3
12xxdx
11
11
12
22
xCBxxAxxx
CBxxA
10
Ax
1
CiBix
dxxx
xiii103
52
dxxx
x25
5
55225
525
xxBxA
xxx
xB
xA
73
372
B
Bx
7101075
A
Ax
dx
xx 273
5710
cxx 2log735log
710
xxdxiv 3
12xxdx
11
11
12
22
xCBxxAxxx
CBxxA
10
Ax
1
CiBix
0 1 CB
dxxx
xiii103
52
dxxx
x25
5
55225
525
xxBxA
xxx
xB
xA
73
372
B
Bx
7101075
A
Ax
dx
xx 273
5710
cxx 2log735log
710
xxdxiv 3
12xxdx
11
11
12
22
xCBxxAxxx
CBxxA
10
Ax
1
CiBix
0 1 CB
dx
xx
x 11
2
dxxx
xiii103
52
dxxx
x25
5
55225
525
xxBxA
xxx
xB
xA
73
372
B
Bx
7101075
A
Ax
dx
xx 273
5710
cxx 2log735log
710
xxdxiv 3
12xxdx
11
11
12
22
xCBxxAxxx
CBxxA
10
Ax
1
CiBix
0 1 CB
dx
xx
x 11
2
cxx 1log21log 2
11 22 xx
xdxv
11 22 xx
xdxv xxDCxxBxxA
xxx
xDCx
xB
xA
222
2222
1111
11111
11 22 xx
xdxv xxDCxxBxxA
xxx
xDCx
xB
xA
222
2222
1111
11111
21121
B
Bx
11 22 xx
xdxv xxDCxxBxxA
xxx
xDCx
xB
xA
222
2222
1111
11111
21121
B
Bx
iDiCix
22
11 22 xx
xdxv xxDCxxBxxA
xxx
xDCx
xB
xA
222
2222
1111
11111
21121
B
Bx
iDiCix
22
21 0 DC
11 22 xx
xdxv xxDCxxBxxA
xxx
xDCx
xB
xA
222
2222
1111
11111
21121
B
Bx
iDiCix
22
21 0 DC
0
021
212
020
A
A
DBAx
11 22 xx
xdxv
dxxx 12
112
122
xxDCxxBxxA
xxx
xDCx
xB
xA
222
2222
1111
11111
21121
B
Bx
iDiCix
22
21 0 DC
0
021
212
020
A
A
DBAx
11 22 xx
xdxv
dxxx 12
112
122
xxDCxxBxxA
xxx
xDCx
xB
xA
222
2222
1111
11111
21121
B
Bx
iDiCix
22
dx
xx
111
21
22 2
1 0 DC
0
021
212
020
A
A
DBAx
11 22 xx
xdxv
dxxx 12
112
122
xxDCxxBxxA
xxx
xDCx
xB
xA
222
2222
1111
11111
21121
B
Bx
iDiCix
22
dx
xx
111
21
22
cxx
11
tan11
21
21 0 DC
0
021
212
020
A
A
DBAx
11 22 xx
xdxv
dxxx 12
112
122
xxDCxxBxxA
xxx
xDCx
xB
xA
222
2222
1111
11111
21121
B
Bx
iDiCix
22
dx
xx
111
21
22
cxx
11
tan11
21
cxx
1tan
11
21
21 0 DC
0
021
212
020
A
A
DBAx
11 22 xx
xdxv
dxxx 12
112
122
xxDCxxBxxA
xxx
xDCx
xB
xA
222
2222
1111
11111
21121
B
Bx
iDiCix
22
dx
xx
111
21
22
cxx
11
tan11
21
cxx
1tan
11
21
21 0 DC
0
021
212
020
A
A
DBAx
Exercise 2G; 1, 3, 5, 7 to 21
