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Math Help - integrate of sqrt tanx

  1. #1
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    integrate of sqrt tanx

    My question is about this integral:



    After using the substitution, u2 = tan(x), I got,



    Next, I tried the partial fraction expansion. But it turned pretty ugly. Is there any easier way of doing it?


    I got a partial solution
    There is;










    how is

    integration of 2u^2/(u^4 + 1).du?

    it is integration of 2u^3/(u^4 + 1)

    equal to
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  2. #2
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    Quote Originally Posted by raj007 View Post
    My question is about this integral:



    After using the substitution, u2 = tan(x), I got,



    Next, I tried the partial fraction expansion. But it turned pretty ugly. Is there any easier way of doing it?


    I got a partial solution
    There is;










    how is

    integration of 2u^2/(u^4 + 1).du?

    it is integration of 2u^3/(u^4 + 1)

    equal to
    Click on Show steps: integrate Sqrt[Tan[x]] - Wolfram|Alpha
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