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dxxSin 2
dxSinx dxCosx dxTanx dxCotx dxSecx dxCscx
dxxCos 2 dxxTan 2 dxxCot 2 dxxSec 2 dxxCsc 2
dxxSin3 dxxCos 3 dxxTan 3 dxxCot 3 dxxSec3 dxxCsc 3
dxxSin 4 dxxCos 4 dxxTan 4 dxxCot 4 dxxSec 4 dxxCsc 4
dxxSin5 dxxCos 5 dxxTan 5 dxxCot 5 dxxSec5 dxxCsc 5
CxCosdxSinx
dxSinx
CxSindxCosx
dxxCos
CxCosdxTanx ||ln
CxSecdxxTan ||ln
or
dxxTan
CxSindxxCot ||ln
dxxCot
CxTanxSecdxxSec ||ln
dxxSec
CxCotxCscdxxCsc ||ln
CxCotxCscdxxCsc ||ln
or
dxxCsc
dxxSin 2
Keyword: Use Double Angle Formulas
CxSinxdxxCosdxxCosdxxSin
22
21)21(
21
2)21(2
dxxCos 2
Keyword: Use Double Angle Formulas
CxSinxdxxCosdxxCosdxxCos
22
21)21(
21
2)21(2
dxxTan 2
Keyword: Use Pythagorean Identities
CxxTandxxSecdxxTan )1( 22
dxxCot 2
Keyword: Use Pythagorean Identities
CxxCscdxxCscdxxCot )1( 22
dxxSec 2
CxTandxxSec 2
dxxCsc 2
CxCotdxxCsc 2
dxxSin3
CxCosCosxdxSinxxCosdxSinx 32
31.
Keywords: Break into a single sine term and the left-over terms; Then use a Pythagorean Identity on the left-over terms.
dxSinxxCosdxSinxxSindxxSin )1(. 223
dxxCos 3
CxSinSinxdxCosxxSindxCosx 32
31.
Keywords: Break into a single cosine term and the left-over terms; Then use a Pythagorean Identity on the left-over terms.
dxCosxxSindxCosxxCosdxxCos )1(. 223
dxxTan 3
CCosxxTandxTanxdxxSecTanx ||ln21. 22
Keywords: Break into a tangent squared term and the left-over terms; Then use a Pythagorean Identity on the tangent squared term.
dxxSecxTandxxTanTanxdxxTan )1(. 223
dxxCot 3
CSinxxCotdxCotxdxxCscCotx ||ln21. 22
Keywords: Break into a cotangent squared term and the left-over terms; Then use a Pythagorean Identity on the cotangent squared term.
dxxCscxCotdxxCotCotxdxxCot )1(. 223
dxxSec3
dxxSecSecxdxxSecI 23 .dxTanxSecxdu
Secxu
Keywords: Special use of Integration by Parts
xTanvdxxSecdv
2
dxxSecSecxTanxSecxdxxTanSecxTanxSecx )1( 22
dxSecxdxxSecTanxSecx 3
||ln TanxSecxITanxSecxI
||ln2 TanxSecxTanxSecxI
CTanxSecxTanxSecxI ||ln21
21
vduuv
dxxCsc 3
dxxCscCscxdxxCscI 23 .dxCotxCscxdu
Cscxu
Keywords: Special use of Integration by Parts
CotxvdxxCscdv
2
dxxCscCscxCotxCscxdxxCotCscxCotxCscx )1( 22
dxCscxdxxCscCotxCscx 3
||ln CotxCscxICotxCscxI
||ln2 CotxCscxCotxCsxxI
CCotxCscxCotxCscxI ||ln21
21
vduuv
dxxSin 4
dxxCosxCosdxxCosdxxSin )2221(41
221 2
24
dxxCosxCosdxxCosxCos 42122
23
41
2)41(221
41
Keywords: Use Double-Angle Formulas twice
CxSinxSinx
4
812
23
41
dxxCos 4
dxxCosxCosdxxCosdxxCos )2221(41
221 2
24
dxxCosxCosdxxCosxCos 42122
23
41
2)41(221
41
Keywords: Use Double-Angle Formulas twice
CxSinxSinx
4
812
23
41
dxxTan 4
dxxSecxTandxxTandxxSecxTan )1(31 23222
dxxSecxTandxxTanxTandxxTan )1(. 22224
Keywords: Break in to a tangent squared term and the left-over terms. Use Pythagorean Identity on the tangent squared term
CxTanxxTan 3
31
dxxCot 4
dxxCscxCotdxxCotdxxCscxCot )1(31 23222
dxxCscxCotdxxCotxCotdxxCot )1(. 22224
Keywords: Break in to a cotangent squared term and the left-over terms. Use Pythagorean Identity on the cotangent squared term.
CxCotxxCot 3
31
dxxSec 4
CxTanTanxdxxSecxTandxxSec 3222
31
xdxSecxTandxxSecxSecdxxSec 22224 )1(.
Keywords: Break in to a secant squared term and the left-over terms. Use Pythagorean Identity on the left-over terms.
dxxCsc 4
CxCotCotxdxxCscxCotdxxCsc 3222
31
xdxCscxCotdxxCscxCscdxxCsc 22224 )1(.
Keywords: Break in to a cosecant squared term and the left-over terms. Use Pythagorean Identity on the left-over terms.
dxxSin5
dxSinxxCosdxSinxxSindxxSin 2245 )1(.
dxSinxxCosdxSinxxCosdxSinxdxSinxCosxCos 4242 2)21(
Keywords: Break into a single sine term and the left-over terms; Then use Pythagorean Identity on the left-over terms.
CxCosxCosCosx 53
51
32
dxxCos 5
dxCosxxSindxCosxxCosdxxCos 2245 )1(.
dxCosxxSindxCosxxSindxCosdxCosxSinxSin 4242 2)21(
Keywords: Break into a single cosine term and the left-over terms; Then use Pythagorean Identity on the left-over terms.
CxSinxSinSinx 53
51
32
dxxTan 5
dxxSecxTandxTanxTandxxTan )1(. 23235
dxxTanTanxxTandxxTandxxSecxTan 24323 .41
Keywords: Break into a tangent squared term and the left-over terms; Then use Pythagorean Identity on the tangent squared terms.
dxTanxdxxSecTanxxTandxxSecTanxxTan 2424
41)1(
41
CCosxxTanxTan ||ln21
41 24
dxxCot 5
dxxCscxCotdxCotxCotdxxCot )1(. 23235
dxxCotCotxxCotdxxCotdxxCscxCot 24323 .41
Keywords: Break into a cotangent squared term and the left-over terms; Then use Pythagorean Identity on the cotangent squared term.
dxCotdxxCscxCotxCotdxxCscCotxxCot 2424
41)1(
41
CSinxxCotxCot ||ln21
41 24
dxxSec5
Keywords: Special use of Integration by Parts
dxxCsc5
Keywords: Special use of Integration by Parts
CosxSinxdxd
)( SinxCosxdxd
)(
xSecTanxdxd 2)( xCscCotx
dxd 2)(
TanxSecxSecxdxd
)( CotxCscxCscxdxd
)(
122 CosSin
22 1 TanSec
22 1 CotCsc
222 SinCosCos
122 2 CosCos
2212 SinCos
vduuvudv
