x2 t04 05 trig substitutions (2011)
TRANSCRIPT
Trig Substitutions
Trig Substitutions22 xa tan use ax
Trig Substitutions22 xa tan use ax 22 xa cosor sin use axax
Trig Substitutions22 xa tan use ax 22 xa cosor sin use axax
22 ax sec use ax
dx
xai
22
1 e.g.
dx
xai
22
1 e.g.
dx
xai
22
1 e.g.
dadxax
2sectan
222
2
tansec
aada
dx
xai
22
1 e.g.
dadxax
2sectan
222
2
tansec
aada
22
2
secseca
da
dsec
dx
xai
22
1 e.g.
dadxax
2sectan
222
2
tansec
aada
22
2
secseca
da
dsec
c tanseclog
dx
xai
22
1 e.g.
dadxax
2sectan
222
2
tansec
aada
22
2
secseca
da
dsec
c tanseclog
x
a
22 xa
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
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
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
dx
xxii
21
dx
xxii
21
ddx
xcos
sin
dx
xxii
21
ddx
xcos
sin
2sin1cossin d
dx
xxii
21
ddx
xcos
sin
2sin1cossin d
2coscossin d
dsin
dx
xxii
21
ddx
xcos
sin
2sin1cossin d
2coscossin d
dsin
c cos
dx
xxii
21
ddx
xcos
sin
2sin1cossin d
2coscossin d
dsin
c cos
x1
21 x
dx
xxii
21
ddx
xcos
sin
2sin1cossin d
2coscossin d
dsin
c cos
x1
21 x
cx 21
2 3iii x dx
2 3iii x dx2
3 tan
3 sec
x
dx d
2 3iii x dx2
3 tan
3 sec
x
dx d
2
3
3 sec 3 sec
3 sec
d
d
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
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
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
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
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
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
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
22 2 32 3 3 3log
3 3x xx dx x x c
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
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
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