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Integrating Derivative on Function
Integrating Derivative on Function
dxxfxf cxf log
Integrating Derivative on Function
dxxfxf cxf log
e.g. (i) dx
x371
Integrating Derivative on Function
dxxfxf cxf log
e.g. (i) dx
x371
dxx37
331
Integrating Derivative on Function
dxxfxf cxf log
e.g. (i) dx
x371
dxx37
331
cx 37log31
Integrating Derivative on Function
dxxfxf cxf log
e.g. (i) dx
x371
dxx37
331
58
xdxii
cx 37log31
Integrating Derivative on Function
dxxfxf cxf log
e.g. (i) dx
x371
dxx37
331
58
xdxii
588
81
xdx
cx 37log31
Integrating Derivative on Function
dxxfxf cxf log
e.g. (i) dx
x371
dxx37
331
58
xdxii
588
81
xdx
cx 58log81 cx 37log
31
Integrating Derivative on Function
dxxfxf cxf log
e.g. (i) dx
x371
dxx37
331
58
xdxii
588
81
xdx
cx 58log81
dx
xxiii
2 6
5
cx 37log31
Integrating Derivative on Function
dxxfxf cxf log
e.g. (i) dx
x371
dxx37
331
58
xdxii
588
81
xdx
cx 58log81
dx
xxiii
2 6
5
dx
xx
26
61
6
5
cx 37log31
Integrating Derivative on Function
dxxfxf cxf log
e.g. (i) dx
x371
dxx37
331
58
xdxii
588
81
xdx
cx 58log81
dx
xxiii
2 6
5
cx 2log61 6
dx
xx
26
61
6
5
cx 37log31
dxx
iv51
dxx
iv51
dxx5
551
dxx
iv51
dxx5
551
cx 5log51
dxx
iv51
dxx5
551
cx 5log51
OR dxx1
51
dxx
iv51
dxx5
551
cx 5log51
OR dxx1
51
cx log51
dxx
iv51
dxx5
551
cx 5log51
OR dxx1
51
cx log51
dx
xx v
1214
dxx
iv51
dxx5
551
cx 5log51
OR dxx1
51
cx log51
dx
xx v
1214 rdenominatoorder numeratororder
dxx
iv51
dxx5
551
cx 5log51
OR dxx1
51
cx log51
dx
xx v
1214 rdenominatoorder numeratororder
divisionpolynomial
dxx
iv51
dxx5
551
cx 5log51
OR dxx1
51
cx log51
dx
xx v
1214 rdenominatoorder numeratororder
divisionpolynomial
124
21412
xxx
dxx
iv51
dxx5
551
cx 5log51
OR dxx1
51
cx log51
dx
xx v
1214 rdenominatoorder numeratororder
divisionpolynomial
124
21412
xxx
dx
x 1212
dxx
iv51
dxx5
551
cx 5log51
OR dxx1
51
cx log51
dx
xx v
1214 rdenominatoorder numeratororder
divisionpolynomial
124
21412
xxx
dx
x 1212
cxx 12log212
dxx
xvi
2
12 12
212 1log x
dxx
xvi
2
12 12
212 1log x
dxx
xvi
2
12 12
2log5log
212 1log x
dxx
xvi
2
12 12
2log5log
25log
212 1log x
dxx
xvi
2
12 12
2log5log
xx
xx viilog integrate
hence and log ateDifferenti 2
3
25log
212 1log x
dxx
xvi
2
12 12
2log5log
xx
xx viilog integrate
hence and log ateDifferenti 2
3
233 3log1log xxx
xxxdxd
25log
212 1log x
dxx
xvi
2
12 12
2log5log
xx
xx viilog integrate
hence and log ateDifferenti 2
3
233 3log1log xxx
xxxdxd
xxx log3 22
25log
212 1log x
dxx
xvi
2
12 12
2log5log
xx
xx viilog integrate
hence and log ateDifferenti 2
3
233 3log1log xxx
xxxdxd
xxx log3 22
25log cxxdxxxx loglog3 322
212 1log x
dxx
xvi
2
12 12
2log5log
xx
xx viilog integrate
hence and log ateDifferenti 2
3
233 3log1log xxx
xxxdxd
xxx log3 22
25log cxxdxxxx loglog3 322
cdxxxxdxxx 232 loglog3
212 1log x
dxx
xvi
2
12 12
2log5log
xx
xx viilog integrate
hence and log ateDifferenti 2
3
233 3log1log xxx
xxxdxd
xxx log3 22
25log cxxdxxxx loglog3 322
cdxxxxdxxx 232 loglog3
cxxxdxxx 332
91log
31log
212 1log x
Exercise 12D; 1 to 12 ace in all, 14a*
Exercise 12E; 1 to 6 all, 7 to 21 odds, 22abc*, 23*
dxx
xvi
2
12 12
2log5log
xx
xx viilog integrate
hence and log ateDifferenti 2
3
233 3log1log xxx
xxxdxd
xxx log3 22
25log cxxdxxxx loglog3 322
cdxxxxdxxx 232 loglog3
cxxxdxxx 332
91log
31log