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Thread: Hard Integration

  1. #1
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    Hard Integration

    Hello all
    Could any one tell me which technique is suitable to solve this integration ? i will be thankful .
    Best regards
    Attached Thumbnails Attached Thumbnails Hard Integration-142.jpg  
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  2. #2
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    Re: Hard Integration

    Multiply both numerator and denominator by \sqrt{tan(x)}- \sqrt{cot(x)}.
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  3. #3
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    Re: Hard Integration

    I did this but no reduction , if you have a final result with steps i will thankful if you can give it to me :-)
    Best regards
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  4. #4
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    Re: Hard Integration

    Are you looking for the integral defined over real numbers or over complex numbers? Because over real numbers, the function is not defined over large chunks of the reals. Over complex numbers, the problem becomes a little different.

    Over the reals, you can do a small simplification by multiplying top and bottom by $\sqrt{\sin x \cos x}$. This will give you:

    $\displaystyle \int \dfrac{\sqrt{\sin x} + \sqrt{\cos x}}{\sin x + \cos x}dx$

    But, over the complex numbers, this simplification is not quite as straightforward. I am not sure I know a good technique for solving this problem.
    Last edited by SlipEternal; Jul 25th 2017 at 01:04 PM.
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  5. #5
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    Re: Hard Integration

    Thanks Slip for replay
    Also i did this modification , but still unsolvable :-(

    Any idea ? in any domain , real , complex , etc
    Best regards
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