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Trig Integrals
Trig Integrals(1) Standard Integrals
caxa
axdx cos1sin
Trig Integrals(1) Standard Integrals
caxa
axdx cos1sin
caxa
axdx sin1cos
Trig Integrals(1) Standard Integrals
caxa
axdx cos1sin
caxa
axdx sin1cos
caxa
axdx tan1sec2
Trig Integrals(1) Standard Integrals
caxa
axdx cos1sin
caxa
axdx sin1cos
caxa
axdx tan1sec2
dxaxaxaxdx
cossintan
Trig Integrals(1) Standard Integrals
caxa
axdx cos1sin
caxa
axdx sin1cos
caxa
axdx tan1sec2
dxaxaxaxdx
cossintan
caxa
ORcaxa
seclog1 coslog1
xx nn cosor sin2
xx nn cosor sin2
xdxsin cx cos
xx nn cosor sin2
xdxsin
xdx2sin
cx cos
xx nn cosor sin2
xdxsin
xdx2sin dxx2cos121
cx cos
xx nn cosor sin2
xdxsin
xdx2sin dxx2cos121
cxx
2sin
21
21
cx cos
xx nn cosor sin2
xdxsin
xdx2sin dxx2cos121
cxx
2sin
21
21
cx cos
xdx3sin
xx nn cosor sin2
xdxsin
xdx2sin dxx2cos121
cxx
2sin
21
21
cx cos
xdx3sin xdxx 2sinsin
xx nn cosor sin2
xdxsin
xdx2sin dxx2cos121
cxx
2sin
21
21
cx cos
xdx3sin xdxx 2sinsin
dxxx 2cos1sin
xx nn cosor sin2
xdxsin
xdx2sin dxx2cos121
cxx
2sin
21
21
cx cos
xdx3sin xdxx 2sinsin
dxxx 2cos1sinxdxdu
xusin
cos
xx nn cosor sin2
xdxsin
xdx2sin dxx2cos121
cxx
2sin
21
21
cx cos
xdx3sin xdxx 2sinsin
dxxx 2cos1sinxdxdu
xusin
cos
duu21
xx nn cosor sin2
xdxsin
xdx2sin dxx2cos121
cxx
2sin
21
21
cx cos
xdx3sin xdxx 2sinsin
dxxx 2cos1sinxdxdu
xusin
cos
duu21
cxx
cuu
coscos3131
3
3
xx nn cosor sin2
xdxsin
xdx2sin dxx2cos121
cxx
2sin
21
21
cx cos
xdx3sin xdxx 2sinsin
dxxx 2cos1sinxdxdu
xusin
cos
duu21
cxx
cuu
coscos3131
3
3
xuxx
xx
PowerOddsome power
cosUsecos1sin Substitute
sinsin as Factorise22
2
xdx4sin
xdx4sin dxx 22sin
xdx4sin dxx 22sin
dxx 22cos141
xdx4sin dxx 22sin
dxx 22cos141
dxxx 2cos2cos2141 2
xdx4sin dxx 22sin
dxx 22cos141
dxxx 2cos2cos2141 2
dxxx 4cos1
212cos21
41
xdx4sin dxx 22sin
dxx 22cos141
dxxx 2cos2cos2141 2
dxxx 4cos1
212cos21
41
dxxx 4cos
212cos2
23
41
xdx4sin dxx 22sin
dxx 22cos141
dxxx 2cos2cos2141 2
dxxx 4cos1
212cos21
41
dxxx 4cos
212cos2
23
41
cxxx
4sin
812sin
23
41
xdx4sin dxx 22sin
dxx 22cos141
dxxx 2cos2cos2141 2
dxxx 4cos1
212cos21
41
dxxx 4cos
212cos2
23
41
cxxx
4sin
812sin
23
41
xx
x
PowerEvenpowersome
2cos121sin Substitute
sin as Factorise
2
2
xdx5sin
xdx5sin dxxx 22sinsin
xdx5sin dxxx 22sinsin
dxxx 22cos1sin
xdx5sin dxxx 22sinsin
dxxx 22cos1sinxdxdu
xusin
cos
xdx5sin dxxx 22sinsin
dxxx 22cos1sinxdxdu
xusin
cos
duuu
duu42
22
21
1
xdx5sin dxxx 22sinsin
dxxx 22cos1sinxdxdu
xusin
cos
duuu
duu42
22
21
1
cxxx
cuuu
53
53
cos51cos
32cos
51
32
xx nn cos and sin3
xx nn cos and sin3
Usually done by substitution xuxu cosor sin
xx nn cos and sin3
Usually done by substitution xuxu cosor sin
xdxxi 35 sincos e.g.
xx nn cos and sin3
Usually done by substitution xuxu cosor sin
xdxxi 35 sincos e.g.
xdxxx sincos1cos 25
xx nn cos and sin3
Usually done by substitution xuxu cosor sin
xdxxi 35 sincos e.g.
xdxduxu
sincos
xdxxx sincos1cos 25
xx nn cos and sin3
Usually done by substitution xuxu cosor sin
xdxxi 35 sincos e.g.
xdxduxu
sincos
xdxxx sincos1cos 25
duuu
duuu57
25 1
xx nn cos and sin3
Usually done by substitution xuxu cosor sin
xdxxi 35 sincos e.g.
xdxduxu
sincos
xdxxx sincos1cos 25
duuu
duuu57
25 1
cxx
cuu
68
68
cos61cos
81
61
81
xx nn cos and sin3
Usually done by substitution xuxu cosor sin
xdxxi 35 sincos e.g.
xdxduxu
sincos
xdxxx sincos1cos 25
duuu
duuu57
25 1
cxx
cuu
68
68
cos61cos
81
61
81
powerhigher eUsually th aseither Choose
u
oddpowersBoth
xdxxii 36 cossin
xdxxii 36 cossin
xdxxx cossin1sin 26
xdxxii 36 cossin
xdxxx cossin1sin 26 xdxduxu
cossin
xdxxii 36 cossin
xdxxx cossin1sin 26 xdxduxu
cossin
duuu
duuu86
26 1
xdxxii 36 cossin
xdxxx cossin1sin 26 xdxduxu
cossin
duuu
duuu86
26 1
cxx
cuu
97
97
sin91sin
71
91
71
xdxxii 36 cossin
xdxxx cossin1sin 26 xdxduxu
cossin
duuu
duuu86
26 1
cxx
cuu
97
97
sin91sin
71
91
71
uevenpoweroneoddpowerOne
aseven Choose&
xdxxii 36 cossin
xdxxx cossin1sin 26 xdxduxu
cossin
duuu
duuu86
26 1
cxx
cuu
97
97
sin91sin
71
91
71
uevenpoweroneoddpowerOne
aseven Choose&
xdxxiii 22 cossin
xdxxii 36 cossin
xdxxx cossin1sin 26 xdxduxu
cossin
duuu
duuu86
26 1
cxx
cuu
97
97
sin91sin
71
91
71
uevenpoweroneoddpowerOne
aseven Choose&
xdxxiii 22 cossin dxxx 22 sin1sin
xdxxii 36 cossin
xdxxx cossin1sin 26 xdxduxu
cossin
duuu
duuu86
26 1
cxx
cuu
97
97
sin91sin
71
91
71
uevenpoweroneoddpowerOne
aseven Choose&
xdxxiii 22 cossin dxxx 22 sin1sin
dxxx 42 sinsin
xdxxii 36 cossin
xdxxx cossin1sin 26 xdxduxu
cossin
duuu
duuu86
26 1
cxx
cuu
97
97
sin91sin
71
91
71
uevenpoweroneoddpowerOne
aseven Choose&
xdxxiii 22 cossin dxxx 22 sin1sin
dxxx 42 sinsin
cxxxxx 4sin3212sin
41
832sin
41
21
xdxxii 36 cossin
xdxxx cossin1sin 26 xdxduxu
cossin
duuu
duuu86
26 1
cxx
cuu
97
97
sin91sin
71
91
71
uevenpoweroneoddpowerOne
aseven Choose&
xdxxiii 22 cossin dxxx 22 sin1sin
dxxx 42 sinsin
cxxxxx 4sin3212sin
41
832sin
41
21
cxx 4sin321
81
xdxxii 36 cossin
xdxxx cossin1sin 26 xdxduxu
cossin
duuu
duuu86
26 1
cxx
cuu
97
97
sin91sin
71
91
71
uevenpoweroneoddpowerOne
aseven Choose&
xdxxiii 22 cossin dxxx 22 sin1sin
dxxx 42 sinsin
cxxxxx 4sin3212sin
41
832sin
41
21
cxx 4sin321
81xx
xxevenpowersBoth
22
22
sin1cosor cos1sin Use
xx nn cotor tan4
xx nn cotor tan4
xdxtan cx coslog
xx nn cotor tan4
xdxtan cx coslog
xdx2tan
xx nn cotor tan4
xdxtan cx coslog
xdx2tan dxx 1sec2
xx nn cotor tan4
xdxtan cx coslog
xdx2tan dxx 1sec2
cxx tan
xx nn cotor tan4
xdxtan cx coslog
xdx2tan dxx 1sec2
cxx tan
xdx3tan
xx nn cotor tan4
xdxtan cx coslog
xdx2tan dxx 1sec2
cxx tan
xdx3tan
xdxxdxx
dxxx
tansectan
1sectan2
2
xx nn cotor tan4
xdxtan cx coslog
xdx2tan dxx 1sec2
cxx tan
xdx3tan
xdxxdxx
dxxx
tansectan
1sectan2
2
xdxduxu
2sectan
xx nn cotor tan4
xdxtan cx coslog
xdx2tan dxx 1sec2
cxx tan
xdx3tan
xdxxdxx
dxxx
tansectan
1sectan2
2
xdxduxu
2sectan
xdxudu tan
xx nn cotor tan4
xdxtan cx coslog
xdx2tan dxx 1sec2
cxx tan
xdx3tan
xdxxdxx
dxxx
tansectan
1sectan2
2
xdxduxu
2sectan
xdxudu tan
cxx
cxu
coslogtan21
coslog21
2
2
xdx4tan
xdx4tan
xdxxdxx
dxxx222
22
tansectan
1sectan
xdx4tan
xdxxdxx
dxxx222
22
tansectan
1sectan
xdxduxu
2sectan
xdx4tan
xdxxdxx
dxxx222
22
tansectan
1sectan
xdxduxu
2sectan
xdxduu 22 tan
xdx4tan
xdxxdxx
dxxx222
22
tansectan
1sectan
xdxduxu
2sectan
xdxduu 22 tan
cxxx
cxxu
tantan31
tan31
3
3
xx nn cosecor sec5
xx nn cosecor sec5
xdxsec
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
dxxx
xxxtansec
tansecsec2
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
dxxx
xxxtansec
tansecsec2
cxx tanseclog
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
xdx2sec cx tan
dxxx
xxxtansec
tansecsec2
cxx tanseclog
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
xdx2sec cx tan
xdx3sec
dxxx
xxxtansec
tansecsec2
cxx tanseclog
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
xdx2sec cx tan
xdx3sec xdxx 2secsec
dxxx
xxxtansec
tansecsec2
cxx tanseclog
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
xdx2sec cx tan
xdx3sec xdxx 2secsec xu sec
dxxx
xxxtansec
tansecsec2
cxx tanseclog
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
xdx2sec cx tan
xdx3sec xdxx 2secsec xu sec
dxxx
xxxtansec
tansecsec2
cxx tanseclog
xdxxdu tansec
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
xdx2sec cx tan
xdx3sec xdxx 2secsec xu sec
dxxx
xxxtansec
tansecsec2
cxx tanseclog
xdxxdu tansec xdxdv 2sec
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
xdx2sec cx tan
xdx3sec xdxx 2secsec xu sec
dxxx
xxxtansec
tansecsec2
cxx tanseclog
xdxxdu tansec xdxdv 2sec
xv tan
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
xdx2sec cx tan
xdx3sec xdxx 2secsec xu sec
xdxxxx 2tansectansec
dxxx
xxxtansec
tansecsec2
cxx tanseclog
xdxxdu tansec xdxdv 2sec
xv tan
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
xdx2sec cx tan
xdx3sec xdxx 2secsec xu sec
xdxxxx 2tansectansec
dxxx
xxxtansec
tansecsec2
cxx tanseclog
xdxxdu tansec xdxdv 2sec
xv tan
xxxdxxx
xdxxdxxx
dxxxxx
tanseclogsectansec
secsectansec
1secsectansec
3
3
2
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
xdx2sec cx tan
xdx3sec xdxx 2secsec xu sec
xdxxxx 2tansectansec
cxxxxxdx tanseclogtansecsec2 3
dxxx
xxxtansec
tansecsec2
cxx tanseclog
xdxxdu tansec xdxdv 2sec
xv tan
xxxdxxx
xdxxdxxx
dxxxxx
tanseclogsectansec
secsectansec
1secsectansec
3
3
2
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
xdx2sec cx tan
xdx3sec xdxx 2secsec xu sec
xdxxxx 2tansectansec
cxxxxxdx tanseclogtansecsec2 3
dxxx
xxxtansec
tansecsec2
cxx tanseclog
xdxxdu tansec xdxdv 2sec
xv tan
xxxdxxx
xdxxdxxx
dxxxxx
tanseclogsectansec
secsectansec
1secsectansec
3
3
2
cxxxxxdx tanseclog21tansec
21sec3
xx nn cosecor sec5
xdxsec
dx
xxxxx
tansectansecsec
xdx2sec cx tan
xdx3sec xdxx 2secsec xu sec
xdxxxx 2tansectansec
cxxxxxdx tanseclogtansecsec2 3
dxxx
xxxtansec
tansecsec2
cxx tanseclog
xdxxdu tansec xdxdv 2sec
xv tan
xxxdxxx
xdxxdxxx
dxxxxx
tanseclogsectansec
secsectansec
1secsectansec
3
3
2
cxxxxxdx tanseclog21tansec
21sec3
partsby DonepowersOdd
xdx4sec
xdx4sec dxxx 22 tan1sec
xdx4sec dxxx 22 tan1sec
xdxduxu
2sectan
xdx4sec dxxx 22 tan1sec
xdxduxu
2sectan
duu21
xdx4sec dxxx 22 tan1sec
xdxduxu
2sectan
duu21
cxx
cuu
3
3
tan31tan
31
xdx4sec dxxx 22 tan1sec
xdxduxu
2sectan
duu21
cxx
cuu
3
3
tan31tan
31
xuxx
xx
PowerEvenpowersome
tan Usetan1sec Substitute
secsec as Factorise22
22
xdx4sec dxxx 22 tan1sec
xdxduxu
2sectan
duu21
cxx
cuu
3
3
tan31tan
31
Exercise 2C; 1, 2, 4, 5, 7, 8, 10, 12, 14, 16, 17, 18
xuxx
xx
PowerEvenpowersome
tan Usetan1sec Substitute
secsec as Factorise22
22
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