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Math Help - basic integration help needed

  1. #1
    Junior Member Dergyll's Avatar
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    basic integration help needed

    Hello guys, just finish learning about Derivatives and Limits yesterday, so I thought I could get started on Integration now.

    I've looked in alot of places but can't find out how to integrade a multiplication/division! I mean, addition and subtraction are easy stuff, just distribute the integral sign but how are multiplication, division handled?

    Here:
    Integrate: 3x(Cos(x^3 + 7))
    Integrate: (x+1)/(x-1)

    Thanks for any help!
    Derg
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  2. #2
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    Dear Dergyll,

    In the first integration have you written, \int{3xCos(x^3+7)dx}\mbox{ or }\int{3Cos(x^3+7)dx} Please confirm this and then I will try to help.
    Last edited by Sudharaka; January 8th 2010 at 07:44 AM.
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  3. #3
    Junior Member Dergyll's Avatar
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    Sorry about that,

    your first integration is correct, its a 3 "x" not multiplication.
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  4. #4
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    Dear Dergyll

    2) \int{{\frac{x+1}{x-1}}dx}=\int{\frac{x-1+2}{x-1}}dx=\int{dx}+2ln\mid{x-1}\mid+C=x+2ln\mid{x-1}\mid+C

    I shall try to do your first sum when time permits. But for the moment the answer escapes me.
    Last edited by Sudharaka; January 8th 2010 at 08:05 AM.
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  5. #5
    Senior Member Shanks's Avatar
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    \int{3xCos(x^3+7)dx} cann't be expressed as elementary function, see Wolfram.
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  6. #6
    Junior Member Dergyll's Avatar
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    Ok, but how do I use the integration by parts method? Why if the problem occurs something like this?

    \int (2x^3+5x+1) (e^2x) dx
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  7. #7
    MHF Contributor
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    Just in case a picture helps...



    ... bigger...

    Spoiler:


    ... where



    ... is the product rule. Straight continuous lines differentiate downwards (integrate up) with respect to x. And integration by parts is a matter of filling out this rule usefully but starting (unlike in differentiation) with one of the lower corners instead of at the top. So the basic pattern is...



    ... and choosing legs crossed or uncrossed is equivalent to asigning u, v, and du and dv

    By the way, other brands of IBP are available. E.g. tabular. And of course this is 'integration by parts thrice', because we have to repeat the pattern until the order of the polynomial goes to zero.

    And I take it this is a new example you're asking about - if you wanted to tackle the 3x(Cos(x^3 + 7)) by parts then, no, no deal. Can't be expressed as elementary means can't be done, basically (roughly).

    __________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
    Last edited by tom@ballooncalculus; January 8th 2010 at 11:23 AM. Reason: btw
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  8. #8
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    Quote Originally Posted by Dergyll View Post
    Integrate: (x+1)/(x-1)
    Derg
    Try u = x-1
    then (x+1)/(x-1) = ? (in terms of u)
    dx = ?
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