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anonymous

  • 5 years ago

Integral of 1 / ( 1 + e ^ x) actual process please... :D

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  1. anonymous
    • 5 years ago
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    Dang you got 103 fans now!

  2. anonymous
    • 5 years ago
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    Hi arman, Try looking at it like this\[\int\limits_{}{}\frac{1}{1+e^x}dx=\int\limits_{}{}\frac{1+e^x-e^x}{1+e^x}dx=\int\limits_{}{}1-\frac{e^x}{1+e^x}dx\]

  3. anonymous
    • 5 years ago
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    Haha, I know!

  4. anonymous
    • 5 years ago
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    \[=x-\log (1+e^x) + c\]

  5. anonymous
    • 5 years ago
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    log == ln always unless a base is made explicit

  6. anonymous
    • 5 years ago
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    It's an arctrig function and x-ln(1+e^x) is e^x/(1+e^x) (chain rule)

  7. anonymous
    • 5 years ago
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    II know that it's arctan of something ><

  8. anonymous
    • 5 years ago
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    The second integral makes use of this fact:\[\int\limits_{}{}\frac{f'(x)}{f(x)}dx=\log f(x)+c\]

  9. anonymous
    • 5 years ago
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    If f(x)=1+e^x, then f'(x)=e^x, which is the form you have after rearranging.

  10. anonymous
    • 5 years ago
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    I'm on my fone so I didn't see half of those equations till after I posted my last post.... lemmy try that... yummy and sec

  11. anonymous
    • 5 years ago
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    Gimmy a sec**

  12. anonymous
    • 5 years ago
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    u substitution then partial fraction decomposition

  13. anonymous
    • 5 years ago
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    I don't get why I can't think of these on my own -.-

  14. anonymous
    • 5 years ago
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    i got an answer of ln(e^x/(e^x+1))+c

  15. anonymous
    • 5 years ago
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    There's one way to check your answer - take the derivative and see if you get back to the integrand.

  16. anonymous
    • 5 years ago
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    yea it does

  17. anonymous
    • 5 years ago
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    just checked it

  18. anonymous
    • 5 years ago
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    Nope, pfd is in the chapter after this (I slipped it previousy and went ahead) so Lucas answer makes perfect sense...

  19. anonymous
    • 5 years ago
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    Lol

  20. anonymous
    • 5 years ago
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    Good work

  21. anonymous
    • 5 years ago
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    Oh boy, integral of e^sqrtx from 0 to 4...

  22. anonymous
    • 5 years ago
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    one sec

  23. anonymous
    • 5 years ago
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    I don't even know what to use on this one...

  24. anonymous
    • 5 years ago
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    2(e^(sqrt(x))(sqrt(x)-1)|(0,4)

  25. anonymous
    • 5 years ago
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    Why?

  26. anonymous
    • 5 years ago
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    have u learned integration by parts yet?

  27. anonymous
    • 5 years ago
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    Yep

  28. anonymous
    • 5 years ago
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    and i take it you know u substitution?

  29. anonymous
    • 5 years ago
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    start with your integral and set u equal to sqrt(x)

  30. anonymous
    • 5 years ago
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    Ok...

  31. anonymous
    • 5 years ago
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    u should get int(2u(e^u)du)

  32. anonymous
    • 5 years ago
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    do you follow me so far?

  33. anonymous
    • 5 years ago
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    You can put the dx in terms of u aswell? (Like I can write 2u instead of 2sqrtx? )

  34. anonymous
    • 5 years ago
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    correct

  35. anonymous
    • 5 years ago
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    from this point you can use integration by parts

  36. anonymous
    • 5 years ago
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    Ok then that makes sense and i can use the uv vdu then.... -.- I'm retarded

  37. anonymous
    • 5 years ago
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    lol its hard to see that without substituting first tho

  38. anonymous
    • 5 years ago
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    No... I'm just retarded. And the answer is 2e^2

  39. anonymous
    • 5 years ago
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    did u evaluate at zero also?

  40. anonymous
    • 5 years ago
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    im getting 2(e^2)+2

  41. anonymous
    • 5 years ago
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    Good point, further testing my retardation.

  42. anonymous
    • 5 years ago
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    lol common mistake

  43. anonymous
    • 5 years ago
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    When you uv vdu sub, can you choose which term is your u and v? I'm pretty sure you can

  44. anonymous
    • 5 years ago
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    usually it depends on what you have

  45. anonymous
    • 5 years ago
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    to remember what to take for u i use "lipet"

  46. anonymous
    • 5 years ago
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    which gives you an order in which to take your u (Lograthims Inverse.trg Polynomials Exponetials Trigonometrics)

  47. anonymous
    • 5 years ago
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    Well I got a badass equation here: integral of (lnx) /x^2 from 1 to 2

  48. anonymous
    • 5 years ago
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    I know I gotta use uv vdu on it

  49. anonymous
    • 5 years ago
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    judging by lipet take log to be your u

  50. anonymous
    • 5 years ago
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    and 1/x^2 to be your dv

  51. anonymous
    • 5 years ago
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    im getting (-ln(x)/x)-(1/x)+c

  52. anonymous
    • 5 years ago
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    your evaluated integral should come out to be (-ln(2)/2)+1/2

  53. anonymous
    • 5 years ago
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    were you able to solve it?

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