ANALISIS MATEMATICO II-FIIA LIC. MAT.JUAN C. CURI GAMARRA

INTEGRAL INDEFINIDA

1.EVALUAR USANDO INTEGRACION POR PARTES

1. 3sec xdx

2. .x arctg xdx

3. 2 .lnx xdx

4. 2.secx xdx

5. 2arcsen xdx

6.3

ln xdx

x

7. 2ln( 1 )x x dx

8. cos(ln )x dx

9. (ln )sen x dx

10. 2.x arctg xdx

11. 2arc sen xdx

12.ln(ln )x

dxx

13.1

.ln1

xx dx

x

14.

2

2cos

xdx

x x senx

15.

2

2

1

1

xx edx

x

16.

2

.

1

xx edx

x

17. 2. 1x arctg x dx

18.2 3/2

.

(1 )

x arc senxdx

x

19.2

arc tg xdx

x

20. 5csc xdx

21.2

1ln

11

x xdx

xx

22. 2 cos( )x xe e dx

23. 1arctg x dx

24. ln 1x x dx

25. 2 lnsen x dx

26.4

3

cos 1

cos

senxe xdx

x

27. 31

4 .x arcsen dxx

28.2 4

.

(1 )

x arctg xdx

x

29.arcsen x

dxx

30.

1

3

xedx

x

31.

2 2

22

sec

sec

x x dx

tg x x x

32. 1arctg x dx

33. 2 2

2

( 1)x

x

e x xdx

x e

34. 2cos . xx e dx

35. . .cosxx e xdx

36. 3

3

ln 2 xdx

x

37.5

2

1.ln

11

x xdx

xx

2.EVALUAR USANDO CAMBIO DE VARIABLE

1. 2

2

ln 1

1

x xdx

x

2. 1 sen x dx

ANALISIS MATEMATICO II-FIIA LIC. MAT.JUAN C. CURI GAMARRA

3.1

dx

x

4.2 32

arctg xdx

x x x

5. 1 cos lnsenxx senx x x x dx

6.4

.cos

2

senx xdx

sen x

7.4

8

9 4

sen xdx

sen x

8.

2 2

2

cos . 1

cos

x tg xdx

sen x x

9.2

1

x

x

edx

e

10. 3secc xdx

11.5 4( 1) x

xdx

x e

12.3 3

ln

(ln 1)

xdx

x x

13.2

6

x x

x

e edx

e

14.5 3xdx

15. 1 cos x dx

16.5

3 8

xdx

x

17.2

21

xdx

x

18. 24 x dx

19. 2 24x x dx

20.2 21

dx

x x

21. 2 21 1

dx

x x

22.4 2 3

dx

x x

23.

3/2

2

(4 5)

2 2

x dx

x x

24.2

3

4x xdx

x

25.

32

6

25xdx

x

26.2cos 4cos 1

sen xdx

x x

27.

2 2

2

4 2 2

2 2 4

x x x x

x x

e e e edx

e e

28.

2 2

2

2 2 2

1 . ln 1 1

1 . 1

xx e xx arctgx x

x x

e e x e

dxx e x e x

ANALISIS MATEMATICO II-FIIA LIC. MAT.JUAN C. CURI GAMARRA

3. EVALUAR USANDO DESCOMPOSICIN EN FRACCIONES PARCIALES:

1.

2

2

3 5

2 1

xdx

x x

2.

3

4 2

6

6 8

xdx

x x

3.

4

32

1

26 2

xdx

x x

4. 3

4 2

2

2 1

x xdx

x x

5.

3 2

2 5

3 4

xdx

x x

6.

2

5 4 3

1

2

x xdx

x x x

7. 2

4 1

xdx

x 8.

3

3

8

xdx

x

9.

3

3

1

1

xdx

x

10. 6 1

xdx

x 11.

3

2

1

1

tdt

t

12.

5

4

1

16

tdt

t

13.

4

24 1

xdx

x 14. 5

1

1dx

x 15.

2

3 25 8 4

xdx

x x x

16.

2

24

1

1

x xdx

x x

17.

3 2

3

7 6 6 12

3 2

x x xdx

x x

18.

2

61

xdx

x

19. 2

3 1

1 2

xdx

x x

20. 221 1 1 2

xdx

x x x 21.

2

3 2

2 2 8

3 3

x xdx

x x x

22.

3

2

3

1

xdx

x x 23.

2

7 1

dx

x x

24.

2 23 5

2 2

xdx

x x

25.

2 2

32

1

1

x xdx

x

26.

2,cos

sen xdx u sen x

x 27.

69

369

, 11

dxu x

x x

28.

3

3 2

1

x dx

x x

29.

2

2

.sec

3 4 sec

x x dx

tg x x 30.

3

2 2 5

dx

x x

31. 2

3 2

1

1

x xdx

x x x

32.

2

4 2

2

5 4

x xdx

x x

33.

5 4 3 2

6 4 2

4 4 8 4

6 12 8

t t t t tdt

t t t

34.3

4 2

4 1

1

x xdx

x x

35.

8 6

dx

x x 36.

5

3 1

x dx

x

ANALISIS MATEMATICO II-FIIA LIC. MAT.JUAN C. CURI GAMARRA

37.

2

999 1

dx

x x 38.

3

9 1

dx

x x 39. 7 1

ctg x dx

sen x

40. 99cos 1

tg x dx

x 41.

4

4

cos

1 cos

x sen x sen x xdx

x x

42. tgh x dx

43. cos . 1

2

x sen xdx

sen x

44.

5 1 cos5dx

sen x x 45.

3

22

1

2

x x dx

x

46.

2

4 2 2

, ,

1 2 1 2 1

tg xdx u tg x

t t t t t

4.EVALUAR LAS EXPRESIONES RACIONALES DE SENO Y COSENO

1. cos

dx

senx x 2.

6c tg xdx 3.

4 2 1

4

dx

sen x sen x

4.

21 cos

dx

x 5. cos cos3

dxdx

x x 6.

2

21

dx

sen x

7. 3cos

dx

senx x 8.

1 3

tgxdx

sen x 9.

cos 2 3

dx

x senx

10. 6cos xdx 11.

3

6cos

sen xdx

x 12.

26 5

dx

senx sen x

13.

3

2

sen xdx

ctg x 14.

52sen xdx

15. 2

cos

senxsen xdx

senx x

16. 21 cos

tgxdx

x 17.

5

2

sec 1

1

xdx

tg x

18.

1 t

dx

gx

19. 5cos

dx

senx x 20.

3

cos xdx

senx sen x 21.

4 2

cos2 3

cos 4

xdx

x ctg x

22. 3

dx

tgx 23.

2

2

sec

5

xdx

tg x tgx 24.

22 3

dx

senx sen x

ANALISIS MATEMATICO II-FIIA LIC. MAT.JUAN C. CURI GAMARRA

25. 6 2 1tg x dx 26.

1

sen xdx

sen x

27. 21 cos cos

sentdt

t t

28. 3cos 2

dx

x senx 29.

2cos 5cos 6

dx

x x 30.

2

2

se

1 cos

n xdx

x

31. 2

2

se

1 cos

n xdx

x 32.

2 24 4

dx

sen x tg x 33.

4 4

2

cos

sen xdx

sen x x

34. 3 2cos

2 3cos

sen x x dx

sen x x

35.

1

1

tg x dx

tg x

36.

2 6 5

dx

sen x senx

37. 2 23 5cos

dx

sen x x 38.

1

2 .cos

tg x dx

sen x x

39.

4 4

2 2

cos

cos

sen x xdx

sen x x

40.

2cos cossenx

dxx x senx

5. INTEGRAR LAS SIGUIENTES EXPRESIONES IRRACIONALES

1. 4

1

xdx

x 2.

2 4

3 1 3 2

dx

x x

3.

3

dx

a bx c

4.

3/2 3/21 1

dx

x x 5.

3

7/3

1

1

xdx

x

6. 3

1

1

x dx

x x

7.

2

3 2 2

dx

x x 8.

4 6

5 2 3

dx

x x

9.

1

1

xx dx

x

10.

3

1 3 1 3

dx

x x 11.

3 2 1

xdx

x x

12.

5 4

x dx

x x

13. 3

dx

x x 14.

2

5 2

xdx

x x 15.

23

23

2

2 3

x dx

x

16.

8 21 2 5

4 2 5

x x dx

x

17.

3 5

4 41 1

dx

x x 18.

1 9

9

xdx

x x

19. 1/7 1/2

8/7 15/14

x x dx

x x

20.

(2 5) 2 3 8 12

dx

x x x 21.

3

1

1

x dx

x

ANALISIS MATEMATICO II-FIIA LIC. MAT.JUAN C. CURI GAMARRA

22. 32

2 2

(2 ) 2

xdx

x x

23.

2sen x senx dx 24. 21 1

1

xdx

x x

25.

2 1

dx

x x 26.

2cos cosx x dx 27.

2cos

3

sen xxdx

sen x

28. 22 4 1

dx

x x x 29.

21 1

dx

x x x 30.

1/3

2/3

1 xdx

x

31. 2 4 4x x

dx

e e 32.

3

23 1

xdx

x

33.

1/23

3

1xdx

x

34. 2

2

2 x xdx

x

6. EVALUAR USANDO CUALQUIER METODO:

1.

3

2

3 8 5

4 7

x xdx

x x

2.

3

2

3 2

1

x xdx

x

3.

2 22 2 1dx

x x

4. 21 1

dx

x x x

5. 2

3 6

4 5

xdx

x x

6.

3

2

3 8 5

4 5

x xdx

x x

7.

2

3 2

2 1

1 1

x x dx

x x x

8. 3 22

dx

x x x

9.

2

2

2 5

4

xdx

x x x x

10.

2 1

1

x x xdx

x

11.

25 4x x dx 12.

1/226 3 1x x dx

13. 2 1x x x dx 14.

1/2

2 4 4x xdx

x

15.

1/225 4

2

x xdx

x

16. 2 2 9x x x dx 17.

1/24 21x x dx

18.

1/222 4 7x x dx