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experimentX Group Title

find the shortest method to evaluate this \[ \int \frac{\sin x}{\sin x + \cos x} \; dx\]

  • 2 years ago
  • 2 years ago

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  1. siddhantsharan Group Title
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    |dw:1347566427407:dw|

    • 2 years ago
  2. experimentX Group Title
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    yeah that it is.

    • 2 years ago
  3. siddhantsharan Group Title
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    Do you know anything shorter?

    • 2 years ago
  4. experimentX Group Title
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    nope ... haven't found any other.

    • 2 years ago
  5. experimentX Group Title
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    just noted how similar these two integrals look like \[ \int \frac{\sin x}{\sin x + \cos x} \; dx \\ \int \frac{\cos x}{\sin x + \cos x} \; dx \]

    • 2 years ago
  6. siddhantsharan Group Title
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    Note one more way. Although the same really, |dw:1347566670806:dw|

    • 2 years ago
  7. mukushla Group Title
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    2I=pi/2 :)

    • 2 years ago
  8. siddhantsharan Group Title
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    ^^ No limits here.

    • 2 years ago
  9. experimentX Group Title
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    well ... pretty clever manipulation on the last problem

    • 2 years ago
  10. mukushla Group Title
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    lol i thought there are ;)

    • 2 years ago
  11. experimentX Group Title
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    yeah ... that is also very nice problem. i wish this one had too http://math.stackexchange.com/questions/198083/integrate-sin3x-sin3x-cos3x/198122#198122

    • 2 years ago
  12. experimentX Group Title
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    interesting technique ...

    • 2 years ago
  13. siddhantsharan Group Title
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    maybe it does. |dw:1347567374847:dw|

    • 2 years ago
  14. experimentX Group Title
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    there is one http://www.wolframalpha.com/input/?i=integrate%20%201/3%2bsin%28x%29/%283%28sin%28x%29%20%2b%20cos%28x%29%29%29%20-%202cos%282x%29/%283%2a%282%20-%20sin%282x%29%29%29 not nice and intuitive though

    • 2 years ago
  15. siddhantsharan Group Title
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    For 2, Taking six + cosx as t, |dw:1347567485586:dw|

    • 2 years ago
  16. experimentX Group Title
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    this is just a back hack

    • 2 years ago
  17. siddhantsharan Group Title
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    back hack?

    • 2 years ago
  18. experimentX Group Title
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    find the answer first ... differentiate the answer to get the get the middle portion.

    • 2 years ago
  19. siddhantsharan Group Title
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    How do you find the answer first?

    • 2 years ago
  20. experimentX Group Title
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    make it easy as much a possible ... that's how i approach most of the problems. i to honest ... i can't work without answer.

    • 2 years ago
  21. siddhantsharan Group Title
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    Okay. Back hack, eh. Hmmmm.

    • 2 years ago
  22. experimentX Group Title
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    Weierstrass substitution gives solution of any type ... but that is the last resort. very ugly method.

    • 2 years ago
  23. siddhantsharan Group Title
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    Agreed.

    • 2 years ago
  24. experimentX Group Title
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    well ... good night!!

    • 2 years ago
  25. siddhantsharan Group Title
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    Yeah. Goodnight. I'll think about this and get back to you tommorow. :)

    • 2 years ago
  26. siddhantsharan Group Title
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    Hold onn. What about the current solution to that, It does work quite easily or not?

    • 2 years ago
  27. siddhantsharan Group Title
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    To the sin^3x/sin^3x + cos^3x

    • 2 years ago
  28. experimentX Group Title
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    there isn't nice manipulation like sin(x)/sin(x)+cos(x) for this one.

    • 2 years ago
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