{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Miscellaneous Substitutions

# Miscellaneous Substitutions - Miscellaneous Substitutions...

This preview shows pages 1–11. Sign up to view the full content.

Miscellaneous Substitutions

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Examples I Rationalizing Substitutions
c x x x x c u u u u c u u u u du u u u u du u u du u u u du u I x u u u x u u x du u dx u x Let x x dx I Example + + - - - = + + - + - = + + - + - = + - + - = + - + = + = + = = = = = = = = + = 1 ln 6 6 3 2 1 ln 6 6 3 2 ] 1 ln 2 3 [ 6 ] 1 1 1 [ 6 1 ] 1 ) 1 [( 6 1 6 6 , ) ( , ) ( 6 ) 1 ( 6 6 3 2 3 2 3 2 3 3 2 3 5 6 2 6 3 3 6 5 6 3 3 1 2 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
c x c u u du u u du u I du u dx u x u x u x Let x x dx I Example + - = + = + = + = = + = = - = - - + - = ) 1 arctan( 2 arctan 2 1 2 2 2 1 1 1 ) 1 ( 1 ) 2 ( 2 3 2 2 3
Examples II Dealing with “rational functions of sinx and cosx”

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 2 1 1 1 1 1 sin cos cos 1 2 1 1 1 2 cos sin 2 sin 1 1 sin , 1 1 sec 1 cos , 1 2 arctan 2 arctan tan : 2 u u u u u x u u u u u x u u u u du dx u x u u on substituti the use We x x x x u x x x x x + - = + - + = - = + = + + = = + = - = + = = + = = = = +
2 1 1 2 2 2 2 2 2 2 1 1 sin , 1 1 sec 1 cos , 1 2 arctan 2 arctan tan : 2 u u u u du dx u x u u on substituti the use We u x x x x x + = - = + = = + = = = = +

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 sin cos cos 1 2 1 1 1 2 cos sin 2 sin : u u u u u x u u u u u x on substituti the use We x x x x + - = + - + = - = + = + + = =
+ - = + + - + = + + - = + - = - + - = + = + = = = = - = 3 10 3 2 1 3 10 3 1 2 1 3 10 3 1 2 5 3 sin 5 3 1 1 cos & 1 2 sin 1 2 arctan 2 arctan tan sin 5 3 ) 1 ( 2 2 2 2 2 2 2 2 2 2 2 2 2 u u du u u u u du I u u u u u x u u x u u x u du dx u x u u Let x dx I Example x x

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
c c c u u du u u u u du I x x x x + - - = + - + - - = + - +
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}