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    i have done a few intergration by parts questions and I am struggling to find why some equations need to have the process done twice

    any explanation would be appreciated.
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    (Original post by mikeabc)
    i have done a few intergration by parts questions and I am struggling to find why some equations need to have the process done twice

    any explanation would be appreciated.
    Hard to explain without a specific example, but note that:
    (i) there's no guarantee that IBP will work at all in the general case!
    (ii) if one of your functions is of the form t^n where n is an integer, and you choose that as the function to differentiate then the IBP process may need numerous repetitions as you reduce the power n to get something that you can integrate directly
    (iii) sometimes when you do an IBP for the first time you end up with something like I = f(x) + J where I is the original integral and J is another integral that you can't work out directly. By applying IBP to J, you may be able to express J in terms of I, which gives you an equation that you can rearrange to solve for I in terms of f(x).
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    (Original post by mikeabc)
    i have done a few intergration by parts questions and I am struggling to find why some equations need to have the process done twice

    any explanation would be appreciated.

    as an aside note, there are things which can help in IBP, for example, reduction formulas, or, like standard integrals , knowing particular formulas for certain ones helps.

    As an example, if you have \int x^{n}exp(x)dx

    the integral of this is just e^x multiplying an alternating series of the successive derivatives of x^n thusly:


    \int x^{4}e^{x}dx = e^{x}(x^{4}-4x^{3}+12x^{2}-24x+24)+c
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    Integration by parts formula: int(u*dv/dx) =uv-int(v*du/dx)

    It's when the integral of v*du/dx is to difficult to integrate by inspection - ie it's (x^2)*(sinx) or something - so you have to use a second integration by parts to put back into the original one
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    that negging wasn`t me, by the way!
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    (Original post by Hasufel)
    that negging wasn`t me, by the way!
    Wow - 3 negs attracted for a comprehensive answer to the OP's question. Someone must be on a downer tonight
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    (Original post by davros)
    Wow - 3 negs attracted for a comprehensive answer to the OP's question. Someone must be on a downer tonight
    My reaction was something like :eek:

    A very precise answer by the way
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    (Original post by davros)
    Wow - 3 negs attracted for a comprehensive answer to the OP's question. Someone must be on a downer tonight
    I plussed you and, hopefully the neggers are not "worth as much as me"

    xx
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    (Original post by Indeterminate)
    My reaction was something like :eek:

    A very precise answer by the way
    I'm up to 4 negs now!

    Maybe revealing that integration by parts isn't a silver bullet that will solve all integration problems is like telling small children that the Easter Bunny doesn't exist
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    (Original post by davros)
    telling small children that the Easter Bunny doesn't exist
    WHAT?

    Well where do the hidden eggs come from then?
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    (Original post by TenOfThem)
    I plussed you and, hopefully the neggers are not "worth as much as me"

    xx
    much appreciated

    Good job I'm not a depressive personality - I never realized an explanation of integration techniques could be so contentious!
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    (Original post by Hunarench95)
    Integration by parts formula: int(u*dv/dx) =uv-int(v*du/dx)

    It's when the integral of v*du/dx is to difficult to integrate by inspection - ie it's (x^2)*(sinx) or something - so you have to use a second integration by parts to put back into the original one
    so if the integral of v*du/dx is hard to intergrate, you repeat the same process where then it will be easier to intergrate
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    (Original post by mikeabc)
    so if the integral of v*du/dx is hard to intergrate, you repeat the same process where then it will be easier to intergrate
    well if your u function is x^2 for example, one application of the integration by parts formula will reduce it to a multiple of x, so you may still have a product that you need to integrate, which means re-applying the IBP formula.

    If you had x^8 as a multiplier, then you might have to apply IBP 7 or 8 times to get something directly integrable - it depends on the "other" function in the original integral!
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    now it makes sense, thanks!!
 
 
 
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