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Thread: Integral Problem - Power of n

  1. #1
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    Integral Problem - Power of n

    This is the book answer









    this is my answer using integration by parts






    How to convert my answer to the book answer?
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  2. #2
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    Re: Integral Problem - Power of n

    I multiplied each side by (a + bu) and I got this





    on the left side, I have this





    then I can move one term to the right side and I add the constants and I got





    but I should get this to have the correct answer





    Where did I go wrong?
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  3. #3
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    Re: Integral Problem - Power of n

    Can anyone help me in this integral? I really wanna know where did I miss the negative sign!
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  4. #4
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    Re: Integral Problem - Power of n

    Stop yelling!!!

    -Dan
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    Re: Integral Problem - Power of n

    Quote Originally Posted by joshuaa View Post
    I multiplied each side by (a + bu) and I got this




    ...


    Where did I go wrong?
    multiplying each side by (a+b u) where u is the variable of integration is not a valid operation
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  6. #6
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    Re: Integral Problem - Power of n

    Thanks for the reply Idea!

    (a + bu) / (a + bu) = 1, where (a + bu) does not equal zero.

    I don't see why it is not valid cuz I am just multiplying by one!
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  7. #7
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    Re: Integral Problem - Power of n

    if I am not mistaken what you are saying is

    $\displaystyle (a+b u)\int \frac{1}{u^n\sqrt{a+b u}} \, du\overset{\text{??}}{=}\int \frac{a+b u}{u^n\sqrt{a+b u}} \, du$
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  8. #8
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    Re: Integral Problem - Power of n

    I did not put any variable outside the integral!

    take (a + bu) inside the integral, then yeah that what I meant
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  9. #9
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    Re: Integral Problem - Power of n

    Quote Originally Posted by joshuaa View Post
    I did not put any variable outside the integral!

    take (a + bu) inside the integral, then yeah that what I meant
    Then where did the a + bu go inside the integral? I'm only seeing the one that Idea noted.

    -Dan
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  10. #10
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    Re: Integral Problem - Power of n

    My bad. It seems that you are both correct.

    topsquark and Idea, thanks for passing by and spending some time in this thread.

    I think that it is the time to close up the thread.

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  11. #11
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    Re: Integral Problem - Power of n

    Quote Originally Posted by joshuaa View Post
    I think that it is the time to close up the thread.
    Agreed.
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