Çözümlü Integral Soruları 2

7/26/2019 zml Integral Sorular 2

1/27

235

AAIDAK LEMLER YAPINIZ.

1. ?4

12

dx

x

2. ?9

322

dxx

x

3. ?5

22

dx

xx

x

4.?16

1

2

2

dx

x

x

5. ?2

12

234

dx

xx

xxx

6. ?)1(

12

2

dx

xx

xx

7. ?)2(

72

dx

xx

x

8. ?)2(

13

5

dx

xx

x

9.

?)1(

13

2

dx

x

xx

10. ?)23)(1(

422

3

dx

xxx

x

11. ?

)2(

1222

3

dx

xx

xx

12. ?tantan

sec23

2

dx

xx

x

13. ?)2)(1(

82

3

dx

xx

x

14. ?)3)(1(

dxee

e

xx

x

15.

?1

1 dx

ex

16. ?)1(

32

dx

xx

x

17. ?)25(

1322

dx

xx

x

18. ?16

14

dx

x

19. ?sinsin

cos3

dx

xx

x

20.

?4

14

dx

x


2/27

236

ZMLER

1.

Cx

xC

x

x

Cxx

dx

xx

x

x

xBxA

dxx

B

x

A

dxxx

dxx

4

2

2

2ln

2

2ln

4

1

2ln4

12ln

4

1

2

4

1

2

4

1

bulunur.4

1Biin2

4

1-Aiin2

1)2()2(

22

)2)(2(

1

4

1

2.

Cxx

dxx

x

x

xxBxA

dxx

B

x

A

dxxx

xdx

x

x

3ln2

33ln

2

1

3

2

3

3x

2

1

bulunur.2

3

Biin3

2

1Aiin3

32)3()3(

33

)3)(3(

32

9

322

3.

Cxx

dx

x

x

x

xBxxA

dxx

B

x

A

dxxx

xdx

xx

x

5ln5

7ln

5

2

5

5

7

x

5

2

bulunur.5

7-Biin5

5

2Aiin0

2)5(

5

)5(

2

5

22

4.

Cx

xx

Cxxx

dxx

x

x

xBxA

dxx

B

x

Ax

dxxx

dxx

x

4

4ln

8

15

4ln8

154ln

8

15

4

8

15

4x

8

15-

x

bulunur.

8

15Biin4

8

15-Aiin4

15)4()4(

44

)4)(4(

151

16

12

2


3/27

237

5.

Cxxxx

dxxx

xx

x

x

xxBxA

dxx

B

x

Axx

dxxx

xx

dxxx

xxx

1ln3

42ln

3

133

3

1

1

3

4

2

3

13

33

1

bulunur.3

4Biin1

3

13-Aiin2

23)2()1(

123

3

1

)1)(2(

73

3

2

1

3

3

3

2

2

234

6.

Cx

xx

Cxxx

dxxx

x

x

xxxCxxBxxA

dxx

C

x

B

x

A

dxxxx

xxdx

xx

xx

1

1ln

2

1ln

1ln2

11ln

2

1ln

1

2

1

1

2

1

x

1

bulunur.21Ciin1

2

1-Biin-1x

1Aiin0

1)1()1()1(

11

)1)(1(

1

)1(

1

2

2

2

2

7.

Cxx

x

dxxx

x

x

x

xCxxBxAx

dxx

C

x

B

x

Adx

xx

x

2ln4

5

2

7ln

4

5

2

4

5

2

7

x

4

5-

bulunur.4

5-Aiin1

4

5Ciin2

2

7Biin0

7)2()2(

2)2(

7

2

2

22

8.

Cxxx

xxx

dxxxxx

x

x

x

xx

xDxxCxBxAx

dxx

D

x

C

x

B

x

Ax

x

dxxx

xx

dxxx

xdx

xx

x

2ln

8

31

4

1

4

1ln

8

12

2

2

8

31

2

1

4

1

8

1

22

x

bulunur.4

1-B,

8

1A

ve83B-Aiin1

8

1BAiin1

8

31Diin2;

2

1Ciin0

14)2()2(

22

2

)2(

14

2

2

1

)2(

1

2

2

32

2

332

32

2

3

3

34

5

3

5


4/27

238

9.

Cxx

x

dxxx

x

xxCxBxA

dxx

C

x

B

x

A

dxx

xx

2

32

22

32

3

2

)1(2

3

1

31ln

)1(

3

)1(

3

1x

1

bulunur.-3B,1A

ve-1B2Aiin1x

-2BAiin0x

3Ciin1

1)1()1(

)1()1(1

)1(

1

10.

Cx

xx

x

dxxxxx

x

x

xxxDxxC

xxBxxxA

dxx

D

x

C

x

B

x

A

dx

xxx

x

dxxxx

x

2ln3

4

1ln12

5

)1(2

31ln

4

3

2

3

4

1

12

5

)1(

2

3

1

4

3

4

3-Aiin0 x,

3

4Diin2

12

5Ciin1x,

2

3-Biin1

4)1()1()2()1(

)2)(1()2)(1)(1(

21)1(1

)2)(1()1(

4

)23)(1(

4

2

322

2

2

3

22

3

11.

Cx

xx

x

dxxxx

x

x

x

xxxDxxC

xBxxA

dxx

D

x

C

x

B

x

A

dxxx

xxdx

xx

xx

)2(9

112ln

27

20

)1(9

41ln

27

7

)2(

9

11

2

27

20

)1(

9

4

1x

27

7

bulunur.27

20C,

27

7A

ve

9

11-2C-Aiin1

9

2-C-2Aiin0

9

11Diin2x,

9

4-Biin1

12)1()2()1(

)2()2)(1(

)2(2)1(1

)2()1(

12

)2(

12

22

322

22

22

22

3

22

3

12.

Cxx

Cxx

x

Cuu

u

duuu

u

CuuBuAu

duu

C

u

B

u

A

uu

du

u

xu

dxxx

x

cot1lncot

1tanlntan

1tanln

1ln1

ln

1

11

u

1-

bulunur.-1Aiin-1u

1Ciin1u,-1Biin01)1()1(

1

)1(u

du

olur.x.dxsecdudersektan

tantan

sec

2

2

2

223

2

23

2


5/27

239

13.

Cxxxx

dxxx

x

x

xxxxC

xxBxxA

dxx

C

x

B

x

Ax

dxxxx

xx

dxxxx

xdx

xx

x

2ln3

161ln

2

91ln

6

7

2

3

16

1

2

9

1x

6

7

x

bulunur.3

16Ciin2

2

9-Biin1 x,

6

7Aiin1

62)1)(1(

)2)(1()2)(1(

211

)2)(1)(1(

621

22

8

)2)(1(

8

2

2

23

3

2

3

14.

Ce

e

Cee

Cuu

duuu

u

uBuA

duu

B

u

A

dxeu

dxee

e

x

x

xx

x

xx

x

3

1ln

4

1

3ln4

11ln

4

1

3ln4

11ln

4

1

3

4

1

1

4

1

4

1-Biin-3u,

4

1Aiin1

1)1()3(

313)1)(u-(u

du

olur.edudersek

)3)(1(

x

15.

Ce

eCee

Cuuduu

u

BuuA

duu

B

u

A

dxeu

dxee

edx

e

x

x

xx

x

xx

x

x

1ln1lnln

1lnln1

1

u

1

1Aiin0u,-1Biin1

1)1(

11)u(u

du

olur.edudersek

)1(1

1

x

16.

Cxxx

dxxx

x

x

dxx

x

A

xxCBxxA

dxx

CBx

x

Adx

xx

x

arctan1ln2

3ln3

1

1

1

33

1

13

x

3

bulunur.-1C,-3B,3

3)()1(

1)1(

3

2

22

2

2

22

17.

Cx

xx

x

dxx

x

xx

A

xxDCxxBxAx

dxx

DCx

x

B

x

A

dxxx

x

5arctan

125

125ln

50

3

25

1ln

25

3

25

25

1

25

3

25

1

25

3

25

1-D,

25

3-C,

25

1B,

25

3

13)()25()25(

25

)25(

13

2

22

222

22

22


6/27

240

18.

Cx

x

x

Cx

xx

dxxxx

A

xxDCx

xxBxxA

dxx

DCx

x

B

x

A

xxx

dx

xx

dxdx

x

2arctan

16

1

2

2ln

32

1

2arctan

16

12ln

32

12ln

32

1

48

1

232

1

232

1

8

1-D,0C,

32

1B,

32

1

1)2)(2)((

)4)(2()4)(2(

422

)2)(2)(4(

)4)(4(16

1

2

22

2

2

224

19.

Cxx

Cuu

duu

u

A

uCBuuA

duu

CBu

u

A

uu

du

u

xu

dxxx

x

1sinln2

1sinln

1ln2

1ln

1u

1

0C,-1B,1

1)()1(

1)1(u

du

olur.cosx.dxduderseksin

sinsin

cos

2

2

2

2

223

3

20.

Cx

xxx

xxkn

Cxxx

xxx

Cww

uu

dww

dww

w

duu

duu

u

dww

w

duu

u

xu

dxx

x

x

x

A

xDCxxBAx

dxx

DCx

x

BAx

xxxx

dx

xx

dx

xxx

dxdx

x

)1arctan(8

1

)1arctan(8

1

22

22

16

1

)1arctan(8

122ln

16

1

)1arctan(8

122ln

16

1

arctan8

11ln

16

1

arctan8

11ln

16

1

1

8

1

1

8

1

1

81

1

81

1

4

1)1(

8

1

1

4

1)1(

8

1-

dxdwdersek1xw

dxdudersek1

1)1(

41

81

1)1(

41

81

4

1D,

8

1C,

4

1B,

8

1

1]1)1)[((]1)1)[((

1)1(1)1(

)22)(22(

)2()2(

4444

1

2

2

2

2

2

2

22

22

22

22

22

22

22

222

2244


7/27

241

AAIDAK LEMLER YAPINIZ.

1. dxxxx 72 )5)(52(

2. dxx 10)3(

3. dxx 97

4.

dx

x

x3 4

3

1

5. dxe x 25

6. xdx3cos4

7. dxx

x

)sin(ln

8. dxxx

x

34

63

2

9. dxx x 123

10. dxxx

ln

3

11. dxe

x

x 5sin5cos

12. dxxx

0

2sin

13. dxxx 5)1)(3(

14.

dxxx 4

15. dxx

x

32

5

16.

dxx

x

242

17. dxx

xx

4

)ln2()ln3( 2

18.

dxx 9

0

4


8/27

242

ZMLER:

1. dxxxx 72 )5)(52(

C

xx

C

u

du

xxu

8)5(

8u

5)dx(2xdudersek5

8287

2

2. dxx 10)3(

Cx

Cu

du

xu

11)3(

11u

-dxdudersek3

111110

3. dxx 97

Cxx

Cu

duu

xu

21

97)97(2

2

37

1

7

1

7dxdudersek97

2

3

2

1

4. dx

x

x

3 4

3

1

CxCu

duu

dxxu

3 243

2

3

1

34

)1(8

3

3

24

1

4

1

4xdudersek1

5. dxe x 25

CeCedue

xu

xuu

25

51

51

51

5dxdudersek25

6. xdx3cos4

CxCuudu

xu

3sin34

sin3

4cos

3

4

3dxdudersek3

7. dxx

x

)sin(ln

CxCuudu

dxxu

)cos(lncossin

x

1dudersekln

8. dxxx

x

34

632

CxxCuu

du

xxu

34ln23

ln2

3

2

3

42xdudersek34

2

2

9.

dxx

x

12

3

CeCedue

xu

xuu

1

2

2

2

1

2

1

2

1

2xdxdudersek1

10. dxxx

ln3

CxCuu

du

dxxu

lnln3ln33

x

1dudersekln

11. dxe

x

x 5sin5cos

Ce

Cuu

du

dx

x

5sin2

sin5xsin5x

5

11

5

1

5

1

5cos5x.edudersekeu

12.

dxxx

0

2

sin

1)11(2

10coscos

2

1

cos2

1sin

2

1

2xdxdudersek

0

0

2

uudu

xu


9/27

243

13. dxxx 5)1)(3(

Cxx

Cuu

duuudu

xu

3

)1(2

7

)1(

3

2

7

)4(4)u(u

4u3 x ve1ux

dxdudersek1

6767

565

14. dxxx 4

Cxx

Cuu

duuuduuu

xu

2

5

2

3

25

23

2

3

2

1

2

1

)4(5

2)4(

3

8

5

2

3

8

)4()4(

u-4x-dx vedudersek4

15. dxx

x

32

5

Cxx

Cuu

duu

duu

u

xu

4

32ln7

4

32

4

ln7

4

2

7

2

1

2

15

2

3

2

1

2

3-u x2dx vedudersek32

16.

dxx

x

2

42

Cxxx

Cuuu

duu

uduu

xu

2ln8)2(42

)2(

ln842

84

42)-(u

2-uxdx vedudersek2

2

2

2

17. dxx

xx

4

)ln2()ln3( 2

Cxx

Cuu

duuuduuu

dxxu

16

)ln3(

12

)ln3(5

1612

5

)5(41))3(2(

41

3-ulnxvex

1dudersekln3

43

43

322

18.

dxx 9

0

4

15

188

3

16

5

4

)82()82(u

14:u90:

)82(

168)4(

4dersek4

1

42

3

2

5

1

4

2

1

2

31

4

22

uu

duuuduu

x

duudx

uuux

uxxu


10/27

244

AAIDAK LEMLER YAPINIZ

1. dxx

1

1

2. dxx

x

3

2

3. dxx

3

4

3

4. dxxx 6 1

5.

dxx

x

923

6. dxxx

33 21

7.

dxxx

x

1

13

8. dxx 5

9. dxx 3 31

10. dxx 42

11. dx

x

12

1

12. dxx

x

1

13. dxx

x

2

4

14. dxx

x

16

54


11/27

245

ZMLER:

1. dxx

1

1

Cxx

Cuu

duu

du

xu

1ln22

1ln22

122

1u2u

2u.dudxdersek

2. dxx

x

3

2

Cxxx

Cuuu

duu

u

duu

uuduu

xu

3ln3010

3ln3010

3

30102

342.2

u-3u2

2u.dudxdersek

2

2

3. dx

x

3

4

3

Cxxx

Cuuu

duu

uduu

u

duxu

4ln144362

9

4ln144362

9

4

144369

4

9

3udxdersek

3

1

3

1

3

2

2

2

23

4. dxxx 6 1

Cxx

Cuu

duuuduuuu

duux

6

7

6

13

713

61256

56

)1(7

6)1(

13

6

75

136

)66(6.).1(

6udxdersek1

5. dxx

x

9

23

Cxx

Cuu

duuduu

u

xu

958)9(2

582

)586(.22)93(u

2u.dudxdersek9

2

3

3

22

6. dxxx

33 21

Cxx

Cuuduu

du

u

uduu

uu

duxu

1ln33

1ln331

33

1

33

1

3udxdersek

33

2

2

23

7.

dxxx

x

1

13

Cxxxxx

Cuuuuu

duu

uuu

duu

uuduuuu

u

duxu

63633 2

224

2

3

2

255

23

3

56

arctan1ln2

1

24

arctan1ln2

1

24

1

11

166

)1(1

6udxdersek

8. dxx 5

Cxx

Cuu

duuuduuuu

duuxu

35

35

243

3

53

205

5

4

3

20

5

4

)204()204(

)20(4udxdersek5


12/27

246

9. dxx 3 31

Cxx

Cuu

duuuduuuu

duuxu

3

4

3

7

47

3625

253

)31(2

3)31(

7

6

2

3

7

6

)66()66(

)6(6udxdersek31

10. dxx 42

Cx

xx

Cuuu

duuuu

duuuuu

duuu

xu

5

79

579

468

357

357

42

5

64

427

4842

9

8

5

64

7

48

9

8

)64488(

)64488(

)64488u(dx

dersek42

11. dx

x

12

1

Cxx

xx

Cu

uuu

duuuu

duuuu

xu

124833

)12(88

5

)12(48

7

)12(8

483

88

5

48

7

8

)4888488(

)488848(8udx

dersek12

3

57

357

246

357

12. dxx

x

1

C

x

xx

Cuuu

duuu

u

uBuA

duu

B

u

A

du

u

du

xu

1

1ln2

1ln1ln2

1

1

1

12

-1Biin-1uve1Aiin1

2)1()1(

112

1

2

21u

2u

2ududxdersek

22

2

13. dxx

x

2

4

Cxxx

x

Cuuu

u

A

duu

D

u

C

u

B

u

A

duuu

udu

xu

)24(2

1

)24(2

1

24

24ln

4

1

)2(2

1

)2(2

1

2

2ln

4

1

2

1-D,

4

1C,

2

1-B,

4

1

)2(2)2(2

)2()2(

2

)4(u

2u-

-2ududxdersek4

22

22

2

22

2

14. dxxx 16

54

duuu

u

uu

duuuu

udu

u

uu

duxu

222

2

3

4

34

34

2

8

4

10

2

3

2

74

)4)(2)(2(

64204

16

204

4udxdersek

4ln52ln32ln74 444 xxxx

Cx 2

arctan44


13/27

247


1. dxx.3sin

2. dxx.5tan

3. dxxx .4tan4sec5

4. dxxx 2)cos(sin

5. dxx.5cos3 2

6. dxx2)tan2(

7. dxx.sin3

8. dxx

x

5sin35cos

9. dxx

x

sin1cos2

10.

dxx

x

sin1sin

11. dxxx 2)3cot3(csc

12. dxxx .tan5sec2

13. dxx.tan5

14. dxxxxx5)cos)(sincos(sin

15. dxex xsin4).(cos

16. dxxx )3sin(cos.3sin

17. dxx

xx

sin)ln(sin.cos

18.

dxxxx .sec34)tan.(sec

19. dxee xx cos

20. dxxx .3sin.

21.

dxxx .cos2

22. dxexx xsin.cos.sin

23. dxxex .sin

24. dxxx .4cos.3sin

25. dxxxx .tansec.sec

26. dxxx

xx

2cos2sin

2cos2sin

27. dxxe

xxx

sin

cossin


14/27

248

ZMLER:

1. dxx.3sin

Cx

Cuduu

xu

3cos

3

1

cos3

1.sin

3

1

3dxdudersek3

2. dxx.5tan

Cx

Cuduu

xu

5secln5

1

secln5

1.tan

5

1

5dxdudersek5

3. dxxx .4tan4sec5

Cx

Cuduuu

xu

4sec4

5

sec4

5.tan.sec

4

5

4dxdudersek4

4.

dxxx 2)cos(sin

Cxx

C

xu

dxxxxdxxx

dxxxxx

2

2

22

sin

uxu.du2x

cosx.dxduderseksin

.cos.sin2)cos.sin21(

)coscos.sin2(sin

5.

dxx.5cos32

Cxx

Cux

duux

xu

dxxx

dxxdxx

10sin20

3

2

3

sin20

3

2

3.cos

10

1

2

3

10dxdudersek10

.10cos2

3

)10cos1(2

3

2

10cos13

6. dxx2)tan2(

Cxxx

xdxxxx

dxxxx

dxxdxxdx

dxxx

tansecln43

.secsecln44

)1(secsecln44

.tan.tan44

)tantan44(

2

2

2

2

7. dxx.sin3

Cx

x

Cu

xdu

xu

dxxxx

dxxxdxx

dxxxx

dxxxdxxx

3

coscos

3cosux-cos

-sinx.dxdudersekcos

.sin.coscos

.sin.cos.sin

)sin.cos(sin

.sin)cos1(.sin.sin

3

32

2

2

2

22

8.

dxx

x 5sin35cos

Cx

Cuu

du

xu

5sin3ln5

1

ln5

1

5

1

5cos5x.dxdudersek5sin3

9. dx

x

x

sin1

cos2

Cxxdxx

dxx

xxdx

x

x

cos)sin1(

sin1

)sin1)(sin1(

sin1

sin1 2

10. dxx

x

sin1sin

dxx

xxdx

xx

xx

2

2

sin1

sinsin

)sin1)(sin1(

)sin1(sin


15/27

249

Cxxx

dxxx

dxxdxxx

dxxxx

dxx

x

x

x

dxx

xx

tansec

)1(secsec

.tan.tan.sec

)tantan.(sec

)cos

sin

cos

sin(

cos

sinsin

2

2

2

2

2

2

2

2

11. dxxx 2)3cot3(csc

Cxxx

Cxuu

xduuuu

xu

dxxxx

dxxxxx

dxxxxx

_3csc3

23cot

3

2

csc3

2cot

3

2

)cot.csc2(2csc

3dxdudersek3

)13cot.3csc23csc2(

))13(csc3cot.3csc23(csc

)3cot3cot.3csc23(csc

2

2

22

22

12. dxxx .tan5sec2

CxCuduu

dxxxu

23

2

3

2

)tan5(3

2

3

2

.secdudersektan5

13. dxx.tan5

Cx

xx

dxxdxxxx

dxxxu

dxxxduu

uxu

dxxdxxx

dxxxdxxx

secln2

tan

4

tan

.tan.sec.tan4

tan

)1(sectan4

.tan.tan

secdudersektan

.tan.sec.tan

)1(sectan.tan.tan

24

24

24

23

2

323

2323

14. dxxxxx5)cos)(sincos(sin

Cxx

Cu

duu

dxxxxxu

6

65

)cos(sin6

1

6

)sin(cosdudersekcossin

15. dxex xsin4).(cos

CeCedu

xu

xu

sin4ue

cosx.dxduderseksin4

16. dxxx )3sin(cos.3sin

Cx

Cuduu

xu

)3cos(cos3

1

cos3

1.sin

3

1-

-3sin3x.dxdudersek3cos

17. dxx

xx

sin)ln(sin.cos

CxCu

duu

dxxu

2

2

))(ln(sin2

1

2.

sinx

cosxdudersek)ln(sin

18. dxxxx .sec34)tan.(sec

Cx

Cuduu

xu

2

3

2

3

)sec34(9

2

9

2

3

1

xx.tan x.d3secduderseksec34

19. dxee xx cos

Ce

Cuduu

dxeu

x

x

sin

sin.cos

edudersek x


16/27

250

20. dxxx .3sin.

v.du-u.vu.dv

olur.3cos3

1- v,dxdu

derseksin3x.dxdvve

x

xu

Cxxx

dxxxxxx

3sin9

13cos

3

.3cos3

13cos.

3

13sin.

21. dxxx .cos2

v.du-u.vu.dvolur.sinxv,dx.2du

dersekx.dxcosdvve2

x

xu

dxxxxxdxxx .sin2sin.cos22

:olur-cosxv,dxdu

derseksinx.dxdvve

xu

Cxxxxx

dxxxxxx

sin2cos2sin

.coscos2sin

2

2

22.

dxexx xsin.cos.sin

Ceex

Ceeudueeu

dudw

dersekduuw

du

xu

xx

uuuu

sinsin

u

u

u

.sin

..

e v,

edvve

u.e

x.dxcosduderseksin

23. dxxex .sin

Cxexedxxe

dxxexex

dx

eu

dxxexedxx

dx

eu

xxx

xx

x

xx

x

sincos.sin2

.sinsincos-e

olur.sin xvedu

dersekdxxcosdvve

.coscos.sine

olur.x-cos v,edu

sin x.dxdvve

x

x

x

x

24. dxxx .4cos.3sin

dxxxxx

x

dxxxu

.4sin.3cos4

34sin.3sin

4

1x.dxsin3x.cos4

olur.4sin4

1 v,3cos3xdu

dersek.4cosdvve3sin

dxxxxx

xx

x

xu

.3sin.4cos4

34cos.3cos

4

1

4

3

4sin.3sin4

1

olur.4cos4

1- v,-3sin3x.dxdu

derseksin4xdvve3cos

xdxxxxxx 4cos3sin16

94cos3cos

16

34sin3sin

4

1

Cxxxx

xx

4cos3cos16

34sin3sin

4

1

4cos3sin16

7

25. dxxxx .tansec.sec

Cxx

Cudu

dxxxx

xxu

tansec2

22

.tansecsec2

1du

dersektansec

26. dxxx

xx

2cos2sin

2cos2sin

Cxx

Cuu

du

xxu

2cos2sinln2

1

ln2

1

2

1

cos2x)dx--2(sin2xdu

dersek2cos2sin

27. dxxe

xx

x

sin

cossin

pay ve payda exile arplr ,u=1+exsin x alnrsa ;

Cxex

sin1ln BULUNUR.


17/27

251


1. dxex5

2. dxex )32(

3. dxe x2ln

7

1

0

714

4. dxx 327

5. dxe

ee

x

x

x

3

25 3

7

6. dxee xx 4)21(

7. dxee xx 244 )(

8. dxeee xxx 10)1)(1(

9. dxx

xx

1

05

43

10.

dxee xx 53 )31(30

11. dxee

ee

xx

xx

16

)3(8

2

12. dxee xx 31

129 )27(

ZMLER:

1. dxex5

Cedxe xx

55

2. dxex )32( Cexdxedx

xx 3232

3. dxe x2ln

7

1

0

714

7dxdudersek7 xu

ln20:u,2ln7

10: x

2241.22.2

2227

14 02ln2ln0

2ln

0

eeedu

e uu

4. dxx 327

C

CCdu

xu

x

xx

u

49ln

7

7ln7

7ln7.

217

21

2dxdudersek32

32

2

3232

5. dxe

ee

x

x

x

3

25 3

7

Cee

dxedxedxee

xx

xxx

x

27

2737

2

3

49

1

37

13

7


18/27

252

6. dxee xx 4)21(

Ce

Cu

due

dxeu

x

u

x

10

)21(

102

1

2edudersek21

5

5

x

7. dxee xx 244 )(

Ce

xe

dxee

xx

xx

8

2

8

)2(

88

88

8. dxeee xxx 10)1)(1(

Cee

Cuu

duuu

duuuduuu

dxeu

xx

x

12

)1(

11

)1(2

1211

2)2(

)2())1(1(

edudersek1

1211

12111110

1010

x

9. dxx

xx

1

05

43

5

4ln5

1

5

3ln5

2

5

4ln

1

5

3ln

1

5

4ln

5

4

5

3ln

5

3

5

4ln

5

4

5

3ln

5

3

5

4

5

3 10

1

0

xx

xx

dx

10. dxee xx 53 )31(30

duuuuduuu

dxeee

dxeu

xxx

x

)2(9

10)1(9

10

)31()(30

-3edudersek31

56752

52

-x

Ceee

Cuuu

xxx

27

)31(5

63

)31(20

36

)31(5

27

5

63

20

36

5

678

678

11. dxee

ee

xx

xx

16

)3(8

2

dxeeeu xxx )3(2edudersek16 x2

Cee

Cuu

du

xx

168

84

2

2

1

12. dxee xx 31

129 )27(

Cee

Cu

duu

dxeu

dxee

xx

x

xx

4

27)27(

43

1

3edudersek27

)27(

3 33

3

4

3

1

3x3

3

1

33


19/27

253


1. dxx

x

23

2. dxx

57

3. dxx

43

2

4. dxx

x

42

5. dxx

x

23

6. dxx

xx

12

34

7. dxxx

)ln3(1

8. dxxx

x

)ln3(

ln7

9. dxxx

54

12

10. dxxx

681221

2

11. dxxx

)9(

1

12. dxx

x

2cos12sin

13. dx

x

x

2sin1

cos

14. dxe

e

x

x

22

1

15. dxe

e

x

x

21

16. dxe

e

x

x

24

1

17. dxxx

x

122

18.

dxxx

x

522

19. dxxx

x

42162

272

20. dxe

x 211

21. dxe

e

x

x

23

1

22. dxxx

xx

4

69


20/27

254

ZMLER:

1. dxx

x

23

Cx

x

dxxdx

x

dx

x

x

x

2||ln3

.1

33

2

2

2. dxx

57

Cx

Cudu

xu

5ln7

ln7u

7

dxdudersek5

3. dxx

43

2

Cx

dxx

2arctan

2

1.3

2

13

22

4. dxx

x

42

Cx

Cuu

du

xu

4ln2

1

ln2

1

2

1

2x.dxdudersek4

2

2

5. dxx

x

23

Cxxxx

dxx

xx

2ln843

2

842

23

2

6. dxx

xx

12

34

Cxxxxx

dxx

xdx

xdxxx

dxx

xxx

1ln2

1arctan

23

11

1)1(

1

11

223

22

2

2

2

7. dxxx

)ln3(1

CxCuu

du

dxxu

ln3lnlnx

1dudersekln3

8. dxxx

x

)ln3(

ln7

Cxx

Cuuduu

du

u

udu

u

u

dxxu

ln3ln3ln10

ln10110

10)3(7

x

1dudersekln3

9. dxxx

541

2

CxCu

du

u

dx

x

)2arctan(arctan1

1

1)2(

1

22

10. dxxx

681221

2

Cx

Cu

dxx

53arctan

101

5arctan

5

1.

2

1

5)3(

1

2

122

11. dxxx

)9(

1

Cx

Cu

duu

dxxu

3arctan

32

3arctan

3

1.2

3

12

x2

1dudersek

22


21/27

255

12. dxx

x

2cos12sin

Cx

Cuduu

xu

2cos1ln2

1

ln

2

11

2

1-

-2sin2xdxdudersek2cos1

13. dxx

x

2sin1cos

Cx

Cudu

xu

)arctan(sin

arctanu1

1

cosx.dxduderseksin

2

14. dxe

e

x

x

22

1

Ce

Cuduu

dxeu

x

x

2

2x2

1ln

2

1

ln2

11

2

1

2edudersek1

15. dxe

e

x

x

21

Ce

Cuduu

dxeu

x

x

arctan

arctan1

1

edudersek

2

x

16. dxe

e

x

x

24

1

2x2 2edudersek1 xeu dx

Cee

Cuu

duu

duu

u

xx

22

1ln)1(2

1

ln2

1

2

1

11

2

11

2

1

17. dxxx

x

122=

Cx

xCu

u

duuu

duu

u

dxxu

1

11ln

1ln

111

dudersek1

22

18. dxxx

x

522

Cx

xx

Cu

u

duu

duu

udu

xu

2

1arctan

2

152ln

2

1

2arctan

2

14ln

2

1

21

22u1-u

dxdudersek1

2

2

222222

19.

dxxx

x

42162

272

Cx

xx

Cu

u

duuu

udu

u

u

xu

dxx

x

dxxx

x

5

4arctan

5

26218ln

4

7

5arctan

5265ln

27.

21

5

26

5

7

2

1

5

267

2

1

dxdudersek4

5)4(

27

2

1

218

27

2

1

2

2

222

2

2


22/27

256

20. dxe

x 211

CexCee

Cuuduu

udu

A

du

u

CBu

u

Adu

uu

dxeu

xxx

x

1ln1ln2

1ln

1ln2

1ln

1u

1

0C,0B,11)1(

1

edudersek

22

2

2

22

x

21.

dxe

e

x

x

23

1

Cee

Cuu

duu

duu

u

dxeu

xx

x

arctan

arctan

1

11

1

edudersek

22

2

x

22. dxxx

xx

4

69

Cxxx

Cuuudu

u

u

duu

uuduu

uu

uu

dxxu

2

2

22

)4ln(4

4ln24

4

242

4

18122).2(

)4(

96

x2

1dudersek

20 x olmak zere;

41sincos 66 xx denkleminin

kkler toplam aadakilerden hangisidir?

A) 2 B) C)4

9 D) 4 E)

2

5

cos6x + sin6x

=(cos2

x)3

+(1-cos2

x)3

=(cos2x)3+ 1-3cos2x + 3(cos2x)2-(cos2x)3

=3(cos2x)2-3cos2x+1=4

1

12(cos2x)2-12cos2x+3=0

4(cos2x)2-4cos2x+1=0

(2cos2x-1)2=0

2cos2x-1=0

cos2x=2

1

cos x=22

x =4

7,

4

5,

4

3,

4

Toplam : 4


23/27

257


1. dxxex

2. dxxx .sin

3. dxxx .ln

4. dxxx .3cos

5. dxx

x

.ln

5

6. dxx.3arcsin

7. dxx.ln

8. dxxx .arctan.2

9. dxex x32

10. dxxx .5ln3

11. dxx2)(ln

12. dxx3)(ln

13. dxxx 3

14. dxxxx .cos.sin

15. dxx

x2

ln

16. dxex x35

17. dxxx ).cos( 23

18. dxxx .35 47

19. dxx

x.

)5( 22

3

20. dxee xx ).sin( 36

21. dxx

ex x.

)1( 22

32

22. dxxex .cos

23. dxxx .5cos.3sin


24/27

258

ZMLER:

1. dxxex u=x ve dv=exdx dersek

du=dx ve v=ex olur.

Cexe

dxexedxxexx

xxx

2. dxxx .sin u=x ve dv=sin x.dx dersek

du=dx ve v=-cosx olur.

Cxxx

dxxxxdxxx

sincos

.coscos.sin

3. dxxx .ln

u=ln x ve dv=x.dx dersek

2

x v ve

2

x

dxdu olur.

Cx

xx

dxxxx

dxxx

4ln

2

.2

1ln

2.ln

22

2

4. dxxx .3cos

u=x ve dv=cos 3x.dx dersek

du=dx ve v= x3sin3

1 olur.

Cxxx

dxxxxdxxx

3cos9

13sin.

3

1

.3sin3

13sin.

3

1.3cos

5.

dxx

x .

ln5

olur.4x

1- v ve

x

dxdu

dersekx

dxdvveln

4

5

xu

Cxx

x

x

dx

x

xdx

x

x

44

5

45

161

4ln

4

1

4

ln.

ln

6. dxx.3arcsin u=arcsin 3x ve dv=dx dersek

olur.xv ve91

.32

x

dxdu

2

91

.33arcsin..3arcsin

x

dxxxxdxx

Cx

xx

Cuxx

u

du

dxxxu

3

913arcsin.

3

13arcsin.

6

1x.arcsin3x

olur..18dudersek91

2

2

7. dxx.ln u=ln x ve dv=dx dersek

du=x

dx ve v=x olur.

Cxxx

dxxxdxx

ln.

ln..ln

8. dxxx .arctan.2 u=arctan x ve dv=2x.dx dersek

21 x

dxdu

ve v=x2 olur.

Cxxxx

dxx

xx

dxx

xxxdxxx

arctanarctan

.1

11arctan

.1

arctan.arctan.2

2

2

2

2

22


25/27

259

9. dxex x32

u=x2 ve dv=e3x dersek

du=2x.dx ve v=3

3xe

olur.

dxexex

dxex x

xx

3

3232 .

3

2

3

u=x ve dv=e3x dersek

du=dx ve v=3

3xe

olur.

Cexeex

dxeexex

xxx

x

xx

27

2

9

2

3

3

1

3

.

3

2

3

3332

3332

10. dxxx .5ln3 u=ln 5x ve dv=x3dx dersek

4

x v ve

4

x

dxdu olur.

Cx

xx

dxxxx

dxxx

165ln

4

4

15ln

4.5ln

44

34

3

11. dxx2)(ln

u=(ln x)2 ve dv=dx dersek

x v ve.ln.2

dxx

xdu olur.

dxxxxdxx .ln2)(ln)(ln22

u=ln x ve dv=dx dersek

x v ve x

dxdu olur.

Cxxxxx

dxxxxx

2ln.2)(ln

ln.2)(ln

2

2

12. dxx3)(ln

u=(ln x)3 ve dv=dx dersek

x v ve)(ln3 2

dxx

xdu olur.

dxxxxdxx 233 )(ln3)(ln)(ln u=(ln x)2 ve dv=dx dersek

x v veln2

dxx

xdu olur.

dxxxxxx

dxxxxxx

.ln6)(ln3)(ln

).ln2(ln3)(ln

23

23

u=ln x ve dv=dx dersek

x

dxdu ve v=x olur.

Cxxxxxxx 6ln.6)(ln3)(ln 23

13. dxxx 3

olur.)3(3

2 vdx vedu

dersek3xdvve

2

3

x

xu

Cxxx

dxxxxdxxx

2

5

2

3

2

3

2

3

)3(15

4)3(

3

2

)3(32)3(

323

14. dxxxx .cos.sin

olur.sin21 vdx vedu

dersekdxsinx.cosx.dvve

2 x

xu

Cxxxx

dxxxx

dxxxxdxxxx

2sin8

1

4

1sin.

2

1

).2cos1(4

1sin.

2

1

.sin2

1sin.

2

1.cos.sin

2

2

22


26/27

260

15. dxx

x2

ln

olur.x1- v ve

x2.ln xdu

dersekx

1dvve)(ln

2

2

dx

dxxu

dxx

x

x

xdx

x

x.

ln2

)(lnln2

22

olur.1

v vex

dxdu

dersekx

1dve vln

2

x

dxxu

Cxx

x

x

x

x

dx

x

x

x

x

2ln.2)(ln

ln2

)(ln

2

2

2

16. dxex x35

olur.3

v ve3xdu

dersekxdvve3

3

2

23

x

x

edx

dxexu

Ceex

dxexex

dxex

xx

x

x

x

33

333

3

3

3

3

23

5

17. dxxx ).cos( 23

olur.)sin(2

1 v2x.dx vedu

dersek)x.cos(xdve v

2

22

x

dxxu

Cxxx

dxxxxx

dxxx

2

)cos(

2

)sin(

).sin(.2

)sin().cos(

222

222

23

18. dxxx .35 47

olur.18

)3x(5

v ve4xdu

dersek35xdvve

2

3

43

434

dx

dxxxu

Cxxx

dxxxxx

dxxx

135

)35(

18

)35(

)35(9

2

18

)35(

.35

2

5

42

3

44

2

3

432

3

44

47

19. dxx

x.

)5( 22

3

olur.)52(x

1- v2x.dx vedu

dersek)5(x

xdvve

2

22

2

dxxu

dxx

x

.)5( 22

3

dxxx

x

x

5)5(222

2

Cx

x

x

2

5ln

)5(2

2

2

2

20. dxee xx ).sin( 36

olur.cos3

1- v ve3edu

derseksinedvve33x

33x3

x

xx

edx

dxeeu

Ceee

dxeeee

dxee

xxx

xxxx

xx

3

sin

3

cos

coscos3

1

).sin(

333

3333

36


27/27

21. dxx

ex x

.)1( 22

3 2

olur.)1(2

1 v ve)1(2x.edu

dersek)1(x

xdvve

2

2x

22

2

2

2

xdxx

dxexu x

dxexx

exdx

x

ex xxx

2

22

.)1(2

.)1( 2

2

22

3

Cex

ex xx

2

2

2

1

)1(2 2

2

22. dxxex .cos

olur.sinxv veedu

dersekcosx.dxdvve

x

dx

eu x

dxxexedxxe xxx .sinsin.cos

Cxexedxxe

Cxexedxxe

dxxexex

dx

eu

xxe

xxx

xx

x

cossin2

1.cos

cossin.cos2

.coscossine

olur.-cosxv veedu

derseksinx.dxdve v

x

x

23. dxxx .5cos.3sin

x

xu

5sin5

1 v ve3cos3x.dxdu

dersekcos5x.dxdvve3sin

dxxxxx

dxxx

.5sin.3cos5

35sin.3sin

5

1

.5cos.3sin

olur.5cos5

1- vve-3sin3xdu

derseksin5x.dxdvve3cos

x

xu

Cxxxx

dxxx

dxxx

xxxx

dxxxxx

xx

5cos.3cos25

35sin.3sin

5

1

.5cos.3sin25

16

.5cos.3sin25

9

5cos.3cos25

35sin.3sin

5

1

.5cos.3sin5

35cos.3cos

5

1

5

3

5sin.3sin51

Cxxxx

dxxx

5cos.3cos16

35sin.3sin

16

5

.5cos.3sin

Documents

Çözümlü Integral Soruları 2