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9 Integral-part2

9 Integral-part2 - Chapter 3(Integral Calculus 3.5(2 x 1 u...

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Chapter 3 积积 (Integral Calculus) 3.5 积积积积积 积积积积积积积积积 积积积积积积积积积 积积积积积积积 积积积积积积积积积积积
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积积 积积积积积积 20 (2 1) d x x + 2 1, (2 1) 2 , u x du d x dx = + = + = 令令令 20 (2 1) d x x + 21 1 (2 1) 42 x C = + + 20 1 d 2 u u = C x + + = 21 ) 1 2 ( 21 1 2 1 20 1 1 1 2 20 1 u C + = × + + 20 u du
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. 令令令 令令令令令令令令令令 dx x + 2008 ) 1 2 ( ) 1 2 ( ) 1 2 ( 2 1 令令 . 2008 + + = x d x . ) 1 2 ( 4018 1 2009 1 2 1 2 1 2009 2009 2008 c x c u du u + + = + = = du u 2008
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dx x x p 1 . 151 3 2 + du u x d x = + + = 2 1 3 2 1 3 3 1 ) 1 ( ) 1 ( 3 1 C x C u + + = + = 2 3 3 2 3 ) 1 ( 9 2 ) 3 2 ( 3 1
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dx x x 2 ) (ln . 1 , ln 1 . x d dx x = 令令令令 c x c u du u + = + = = 3 3 2 ) (ln 3 1 3 令令 + 2 2 . 6 153 a x dx p ) ( , ) ( 1 1 . 2 2 a x ad dx a x dx a = + = 令令令令 令令 c a x a c u a u du a + = + = + = arctan 1 arctan 1 1 1 2 令令 C x dx x + = + arctan 2 1 1
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) 0 ( 1 . 7 153 2 2 - a dx x a p ) ( , ) ( 1 1 2 a x ad dx dx a x a = - = 令令令令 令令 c a x c u du u + = + = - = arcsin arcsin 1 1 2 令令 C x dx x + = - arcsin 2 1 1
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1 153 5 d (3ln 1) P x x x - 1 1 d(3ln 1) 3 3ln 1 x x = - - 令令 1 ln | 3ln 1| 3 x C = - +
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1 154 8. d 1 x P x e + 1 [1 ]d d(1 ) 1 1 x x x x e x x e e e = - = - + + + ∫ ∫ ln(1 ) x x e C = - + + 1 d d(1 ) 1 1 x x x x e x e e e - - - - = = - + + + ∫ ∫ 令令令令 ln(1 ) x e C - = - + +
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- + = dx x xf c x dx x f p ) 1 ( , ) ( . 9 . 154 2 2 - - - = - ) 1 ( ) 1 ( 2 1 ) 1 ( . 2 2 2 x d x f dx x xf 令令 c x + - - = 2 2 ) 1 ( 2 1 x c x x f 2 ) ( ) ( . ' 2 = + = 令令 c x x dx x x + - = - = 4 2 2 2 1 ) 1 ( 2 令令
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积积积积积 (p155) x d xdx x d xdx de k dx e x d dx x x d dx x x d dx x dx xdx a b ax d a dx kx kx sin cos , cos sin . 7 1 . 6 | | ln 1 . 5 2 1 . 4 1 1 . 3 2 1 . 2 ) 0 )( ( 1 . 1 2 2 = - = = = = - = = + =
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- 2 1 3 ) 2 3 ( 1 . 13 155 dx x p 2 1 2 2 1 3 ) 2 3 ( 1 ) 2 1 )( 2 1 ( ) 2 3 ( ) 2 3 ( 2 1 . x x x d - - - = - - - = 令令 0 ) 2 3 ( 1 4 1 2 1 2 = - = x dx x x p e e 4 4 / 1 ln . 14 156令 4 4 / 1 4 4 / 1 2 / 3 ) (ln 3 2 ln ln e e e e x x d x = = 4 21 ] 8 1 8 [ 3 2 = - = 1 1 2 1 1 1 1 2 dx x x - - = - = -
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P201,17. 积积积积积 8 . 172 ) 6 ( , 3 4 ) ( ' = + = C x x x C 积 : 积积积积积 C ( x ) dx x x x C + = 3 4 ) ( . dx x x + - + = 3 ) 3 3 ( 4 ) 3 ( ] ) 3 ( 3 ) 3 [( 4 2 1 2 / 3 + + - + = x d x x 5 / 2 3/ 2 2 4[ ( 3) 2( 3) ] 5 x x C = + - + + 2 / 3 2 / 5 ) 3 ( 8 ) 3 ( 5 8 ) ( 0 8 . 172 ) 6 ( + - + = = = x x x C C C
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; | ) ( 1 | ln ) ( 1 ) ( ' ) ( ; 1 1 1 ln ) ( . ________ 3 c x f dx x f x f B c x x d x dx x x A + + = + + = = 令令令令令令令令 . | ) ( 1 | ln 2 1 ) ( 1 ) ( ' ) ( ; ) ( arctan ) ( 1 ) ( ' ) ( 2 2 2 c x f dx x f x f D c x f dx x f x f C + + = + + = + C B ,
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9 Integral-part2 - Chapter 3(Integral Calculus 3.5(2 x 1 u...

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