x2 t05 05 trig substitutions (2010)
TRANSCRIPT
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Trig Substitutions
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Trig Substitutions22 xa tan use ax
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Trig Substitutions22 xa tan use ax 22 xa cosor sin use axax
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Trig Substitutions22 xa tan use ax 22 xa cosor sin use axax
22 ax sec use ax
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dx
xai
22
1 e.g.
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dx
xai
22
1 e.g.
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dx
xai
22
1 e.g.
dadxax
2sectan
222
2
tansec
aada
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dx
xai
22
1 e.g.
dadxax
2sectan
222
2
tansec
aada
22
2
secseca
da
dsec
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dx
xai
22
1 e.g.
dadxax
2sectan
222
2
tansec
aada
22
2
secseca
da
dsec
c tanseclog
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dx
xai
22
1 e.g.
dadxax
2sectan
222
2
tansec
aada
22
2
secseca
da
dsec
c tanseclog
x
a
22 xa
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dx
xai
22
1 e.g.
dadxax
2sectan
222
2
tansec
aada
22
2
secseca
da
dsec
c tanseclog
x
a
22 xa
cax
axa
22
log
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dx
xai
22
1 e.g.
dadxax
2sectan
222
2
tansec
aada
22
2
secseca
da
dsec
c tanseclog
x
a
22 xa
cax
axa
22
log
caxxa loglog 22
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dx
xai
22
1 e.g.
dadxax
2sectan
222
2
tansec
aada
22
2
secseca
da
dsec
c tanseclog
x
a
22 xa
cax
axa
22
log
caxxa loglog 22
cxxa 22log
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dx
xxii
21
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dx
xxii
21
ddx
xcos
sin
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dx
xxii
21
ddx
xcos
sin
2sin1cossin d
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dx
xxii
21
ddx
xcos
sin
2sin1cossin d
2coscossin d
dsin
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dx
xxii
21
ddx
xcos
sin
2sin1cossin d
2coscossin d
dsin
c cos
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dx
xxii
21
ddx
xcos
sin
2sin1cossin d
2coscossin d
dsin
c cos
x1
21 x
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dx
xxii
21
ddx
xcos
sin
2sin1cossin d
2coscossin d
dsin
c cos
x1
21 x
cx 21
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2 3iii x dx
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2 3iii x dx2
3 tan
3 sec
x
dx d
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2 3iii x dx2
3 tan
3 sec
x
dx d
2
3
3 sec 3 sec
3 sec
d
d
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2 3iii x dx2
3 tan
3 sec
x
dx d
2
3
3 sec 3 sec
3 sec
d
d
23 sec sec d
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2 3iii x dx2
3 tan
3 sec
x
dx d
2
3
3 sec 3 sec
3 sec
d
d
23 sec sec d secu
sec tandu d 2secdv d
tanv
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2 3iii x dx2
3 tan
3 sec
x
dx d
2
3
3 sec 3 sec
3 sec
d
d
23 sec sec d secu
sec tandu d 2secdv d
tanv
23sec tan 3 sec tan d
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2 3iii x dx2
3 tan
3 sec
x
dx d
2
3
3 sec 3 sec
3 sec
d
d
23 sec sec d secu
sec tandu d 2secdv d
tanv
23sec tan 3 sec tan d 33sec tan 3 sec 3 secd
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2 3iii x dx2
3 tan
3 sec
x
dx d
2
3
3 sec 3 sec
3 sec
d
d
23 sec sec d secu
sec tandu d 2secdv d
tanv
23sec tan 3 sec tan d 33sec tan 3 sec 3 secd
33sec tan 3 sec 3log sec tand
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2 3iii x dx2
3 tan
3 sec
x
dx d
2
3
3 sec 3 sec
3 sec
d
d
23 sec sec d secu
sec tandu d 2secdv d
tanv
23sec tan 3 sec tan d 33sec tan 3 sec 3 secd
33sec tan 3 sec 3log sec tand
x2 3x
3
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2 3iii x dx2
3 tan
3 sec
x
dx d
2
3
3 sec 3 sec
3 sec
d
d
23 sec sec d secu
sec tandu d 2secdv d
tanv
23sec tan 3 sec tan d 33sec tan 3 sec 3 secd
33sec tan 3 sec 3log sec tand
x2 3x
32 2
23 33 3 3log3 3 3 3
x x x xx dx
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22 2 32 3 3 3log
3 3x xx dx x x c
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22 2 32 3 3 3log
3 3x xx dx x x c
2 22 3 3 33 log
2 2 3 3x x x xx dx c
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22 2 32 3 3 3log
3 3x xx dx x x c
2 22 3 3 33 log
2 2 3 3x x x xx dx c
2
2 23 33 log 32 2
x xx dx x x c
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22 2 32 3 3 3log
3 3x xx dx x x c
2 22 3 3 33 log
2 2 3 3x x x xx dx c
2
2 23 33 log 32 2
x xx dx x x c
Exercise 2E; 1, 2, 3, 5, 6, 7, 9, 13, 17, 19, 20