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Math Help - Another Integration by Parts problem I keep getting almost right!

  1. #1
    s3a
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    Another Integration by Parts problem I keep getting almost right!

    My work is attached.

    The final answer in my text book is the same that Wolfram Alpha provides:
    integral (arctan(4x - Wolfram|Alpha))

    but Wolfram Alpha does not show the work for this integThe final answer in my text book is the same that Wolfram Alpha provides:ral; it says "$Aborted" whenever I ask it to show the steps.

    My work is different according to this in Wolfram Alpha: is 1/8 * ln(1 + 16x^2) = 2ln(x^2 +1) ?

    If they are equal, it returns true, otherwise it shows the usual data. And, it does not return true, so they are not equal.

    Any help would be very much appreciated!
    Thanks!
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  2. #2
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    Quote Originally Posted by s3a View Post
    My work is attached.

    The final answer in my text book is the same that Wolfram Alpha provides:
    integral (arctan(4x - Wolfram|Alpha))

    but Wolfram Alpha does not show the work for this integThe final answer in my text book is the same that Wolfram Alpha provides:ral; it says "$Aborted" whenever I ask it to show the steps.

    My work is different according to this in Wolfram Alpha: is 1/8 * ln(1 + 16x^2) = 2ln(x^2 +1) ?

    If they are equal, it returns true, otherwise it shows the usual data. And, it does not return true, so they are not equal.

    Any help would be very much appreciated!
    Thanks!
    you have differentiated arctan(4x) wrongly.

    it should be

    4/(16x^2+1)
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  3. #3
    o_O
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    You made an error when you took the derivative of \tan ^{-1} (4t)
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  4. #4
    s3a
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    Omg! I would have never spotted that mistake! Thanks to both of you! (I had forgotten that you replace the contents of arctan into the x)
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