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Math Help - Integration - Im stumped

  1. #1
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    Integration - Im stumped

    I should know this but I cannot figure it out.

    The problem is.

    integrate Cot[x]/Sqrt[Sin[x]] dx

    I convert the Cot[x] into Cos[x]/Sin[x]

    I assume this problem is done by u-substitution. I cant figure out what to set u = ?

    Thanks for you help.
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  2. #2
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    U sub value

    Just set your U substitution with u=sin(x) and that will get you to the end, good luck.
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  3. #3
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    you can do it without u substitution (unless it is required). Just make the bottom sinx^(3/2) and you should be able to do it no problem ... I personally dont like u substitution too much, too much work.
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  4. #4
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    I have tried that but I get lost.

    So here is where I am at.

    Integral (Cos[x]/Sin[x])/Sqrt[Sin[x]] dx

    Let u = sinx
    du = cosx

    I am not sure how the problem will look after the substitution.
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  5. #5
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    I think I got it.

    (-2)/Sqrt[Sin[x]] + C


    I liked that idea of just combining the Sin's into sin^(3/2).


    Thanks for the help everyone!
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  6. #6
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    yeah thats what I got
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  7. #7
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    Quote Originally Posted by aervid View Post
    you can do it without u substitution (unless it is required). Just make the bottom sinx^(3/2) and you should be able to do it no problem ... I personally dont like u substitution too much, too much work.
    Personally I'd advise that a beginner should always attempt this sort of integral making the substitution suggested earlier.
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