## roselin Group Title evaluate indefinite integrals intergral tan^2x Sec^2x dx one year ago one year ago

1. cinar

tanx=u

2. cinar

take the derivative

3. roselin

derivative of tanx?

4. cinar

both sides

5. cinar

what is it

6. roselin

derivative of tna is sec^2x

7. cinar

sec^2xdx=du

8. cinar

subs. them in int.

9. cinar

if tanx=u then what is tan^2x

10. roselin

u sqre

11. cinar

good

12. cinar

then what is your new int. depends on only u

13. cinar

int. tan^2x Sec^2x dx sec^2xdx=du tan^2x=u^2

14. roselin

csc x^3/ 3 ?

15. cinar

|dw:1355646302656:dw|

16. cinar

what are they in u

17. roselin

u^2 . du

18. cinar

yesssssss..

19. cinar

solve that integral..

20. roselin

1/3 tan^3 x+c ?

21. cinar

you got it..

22. roselin

but i have one question though

23. cinar

shoot it..

24. roselin

|dw:1355639354738:dw|

25. cinar

|dw:1355646949637:dw|

26. roselin

did not get it,s orry

27. cinar

they are the same thing but just different letter..

28. cinar

|dw:1355647192985:dw|

29. roselin

oh okay.

30. cinar

dx or du they are just saying that you are taking int. depends on that variable

31. cinar

|dw:1355647315134:dw|

32. cinar

you can assume that x is just a constant in here..

33. roselin

okay,thanks. i have another problem, will you help me with that?

34. cinar

ok..

35. roselin

thanks

36. roselin

|dw:1355640103615:dw|

37. cinar

|dw:1355647649309:dw|

38. cinar

take derivative

39. roselin

how do you decide which one is "U"?

40. cinar

(:

41. cinar

because I can see that derivative sinx =cosxdx and it is above

42. cinar

|dw:1355647787810:dw|

43. roselin

derivative of sin theta = cos theta d theta

44. cinar

but it is sinsqrt theta

45. roselin

cos sqrt theta d theta

46. cinar

|dw:1355647993776:dw|

47. cinar

one more thing youre missing

48. roselin

what is it?

49. cinar

derivative of sqrt theta

50. roselin

|dw:1355640793032:dw|

51. cinar

|dw:1355648238516:dw|

52. cinar

|dw:1355648283456:dw|

53. roselin

how did you get that half?

54. cinar

|dw:1355648328997:dw|

55. cinar

|dw:1355648354029:dw|

56. cinar

|dw:1355648407558:dw|

57. cinar

58. cinar

|dw:1355648571843:dw|

59. roselin

1/2 integral 1/sin sqrt theta +c?

60. cinar

|dw:1355648717143:dw|

61. cinar

|dw:1355648783325:dw|

62. roselin

confused

63. cinar

what is int. 1/x dx=?

64. roselin

d

65. roselin

x

66. cinar

|dw:1355648969297:dw|

67. roselin

okay

68. cinar

in your case lnu+c put u back in

69. cinar

I gotta go, any question..

70. roselin

so,thats the ans ? after putting the u?

71. cinar

yes, ln(sin sqrt theta)+c is the answer..

72. roselin

okay,thanks a lot

73. cinar

np..