aoristo_olokl

7/24/2019 aoristo_olokl

1/8

:

. :

1. ( )23 4 1x x dx + 2. ( ) 22 5x dx 3. 3x x dx

4. ( )3x x x dx + + 5.3 2

2

5 3x x xdx

x

+ + 6. 3 1x dxx

7. ( )3 23x dxe x x + 8. 2 21 1

dxx x

9.

3

2

1 xdx

x

10.

+ dx

xx 2

2

1

3

1

2 11. 2

x dx 12.3 8

2

xdx

x

++

13. 2x dx 14.dx

x

xx

63223

15.3 2

1x

x aa dxx

+

16.2 2(5 3 )x x dx +

. !"#$ %&$ !%'()*+$ ,

17. -' *)/%) !0+*%&!& f%%' !%) ( ) 2 1f x x= ' & fC ' )*+ '#% !&")/ 23.

18. -' *)/%) !0+*%&!& f%%' !%)1

( )f x

= (0, )x + ' (9) 1f = .

1. -' *)/%) !0+*%&!& f%%' !%) ( ) 3, (1) 6 (0) 4.f x f f= = =

29. -' *)/%) !0+*%&!& f%%' !%)2( ) 12 2f x x= + ' !% !&")/ 11

) /!& 3.

; !


2/8

:

-

. :

1.2

xdx

x ( 2x u =

2. ( )4 2 35 4x x dx+ ( 4 5x t+ =

3.3 22x x dx+ 4.

2 3xe xdx+ 5. ( ) 21x

x

e dxe+

6.3

4

8

1

xdx

x + !. ( )423

6

xdx

x x

+

+ ". ( ) ( )2 34 16 7 2x x x dx +

9. ( )23 2x xdx + 10. 32x dx + 11. dxx ( 2x u =

#$% 1&2&3&4 '.9"'# % !# /; !

2

' *)/%) %


3/8

:

AA - B- -

:

1. ( )3 5x dx + 2. ( )2 1 2x dx +

3.7 5xe dx+ 4. 231 16 dxx+

5.2

1

9 4dx

x 6. 24

1 100dx

x

!.5 2x x dx ". 3x x dx

9. ( )

62 35 1x x dx

+ 10.3(ln )x

dxx

11.

2

3 2

3 4 5

2 5 3

x xdx

x x x

+ ++ + + 12. 221 x dxx+

12* x dx 14* x dx #$% )+ $+ 104& 105& 106 , !C /0.; !


4/8

:

#-/ //-

:

1. lnx dx 2.2xx e dx 3.

2 2(2 1) xx e dx

4.2x x dx 5. xe x dx 6. 3 ln(5 )x x dx

#$% )+ $+ 110& 111& 106 , !C /0.

; !!).115

u dv u v v du =


5/8

727

88 / #/ //-;

? I , , ,> @) A

> B,)A )CA > &$$? ( ).f x

#+ B+ , D)+ , ,>$,> I

1 2 3, , ,......I I I , >) + $)+ B?+ D)A ) ,>+

,> C >) + B?+ 1 2( ) , ( ) , ....f x f x )+ D)+ >E>) >%%) F).

> .D > >) C+ + + ,>+ A >%%)A+

F+ + $% ? + $)+ B?+ C 1 ? 2 ..

)A & )A ? > >) F > ,%)A ,

1. ' > I xdx = > $@ A) )DF) >%%)A+ F+:1

2

1x xI I

= +

,% 4I .

2. > >%%)A F %) :

( )lnI x dx

=

) > ,% 3

I

( )I x dx

= ) > ,% 3I

3. > I x dx

= > $@ A) )DF) >%%)A+ F+:1

2

1x xI I

= +

,% 4I .

4. -' 'D)/E)%) % ''@# %C:

1 21 2

1 1

dx x dxI

x x x

= = +

.F&"&%*/0.


6/8

:

- --

:

G 1.2

2 5dx

x+ 2. 22 1x dxx + 3. 22 51x dxx + 4. 2

3

(5 1)dx

x 5. 23 41x dxx ++ 6. 1 11 1 dxx x +

GG 7. 22 1dx

x 8. 3 222 3

x dxx x x

+ . 2 525 10 1

x dxx x

+ + 19. 2

3

3 2 1

xdx

x x

+ + + 11. ( )( )2

5

1 4

xdx

x x+ + 12. 3 2( 1)dxx x 13. 4 1

dx

x 14. 83 5 2dx x+ ' (!)%) t x=

GGG 15. 2 9

dx

x + 16. 23 616x dxx ++ 17. 2 6 10dxx x + 18. 2

5 1

4 13

xdx

x x

+ 1. 2 8 14 12 34x dxx x+ + 29. 15 3 dxx+

' (!)%)2

xt =

-' *)/%) %' '*'+%@ &*"'%':

21.

5

2 2

xdx

x + 22.5

2

3

1

x xdx

x

+

A'*'D)/"'%' !%$ !)/D)$ 116=121 %0 !C /0.

; !!).121

GGGGGG.' .121


7/8

:

. :

1.

+ dx

xx 22

1

3

1

2

2.dx

x

xx

6

3223

3. dxx

e x

4. dxxx

+

21

5.1 n

n

xdx

x x

+ ll 6. dxee xx

2

2

31

!. +

dx

exxe

e

xx

x

2221

1

(A$)@: H

2I

J I

2

72IH

I

K (I7H

I

2

.

". dxxx 2 9. dxxx3

10.( ) + dxx

x

22

2

1 11. n ,x x dx

l

12. dxxx 13. dxxx

4

3

14. + dxxx

1 15. dxx5

16. +

21

d (> C BCKL

1! *. + 20032003xx

dx (> C 1J2003I2002 K M

1" . dxxxx 32 (A$)@: B3IKB(2IJI

19.( )

21

xxedx

x+ 20. ( ) 31nx

dxx

l

21.2

1 2

x xdx

x

22. ( )21x x

dxx

+


8/8

. 1. > n ,I xdx

= l > $@ A)1n ,I x x I

= l ) > 3I .

2. N*1

, 0( 1)v vI dx x vx x = +

O $@ A):( )

1 1

1 1, 2

1 1 v

I Iv x

= + +

OO ,% 1 2,

. 1. = 41 1 xdx

I )( ) = 242 1 x

dxI .

2. ?:

( )2 21

0, 0,2

I dx a x ax a

=

F. + B>+ )+ F+ (P @ QKQ(I &QR0

+ ;(I&Q >) IQ. > @ + (P &> >) %>A A) $)D) A

(0&1. (A$)@: Q

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