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Thread: Integral Help

  1. #1
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    Default Integral Help

    I've been pulling my hair out over this problem for some time now... was hoping someone could lend a hand?

    I'm solving for the indefinite integral of:

    (t+3)^2/(t^4)

    This is from the "Integration by Substitution" section, so there is a way to do this by substitution... I just keep getting stuck.

    Any help would be appreciated

    Thanks
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    err, expand the quadratic then distribute the denominator.

    then.. http://www.wolframalpha.com/input/?i=integrate+[[t%2B3]^2]%2F[t^4]
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    WOLFRAM YEAH!

    Here is a proper link just click the show steps button to see how WFA did the problem. Nava2, I dont think the forums like your link or maybe it just miss typed.

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    Nope, the forums did not like it. Haha, its the use of brackets instead of using parenthesis.
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    Default

    Ah thanks a lot man. The problem was throwing me off since I was thinking in terms of substitution.

    And wow... that site is really legit. Definitely using that a lot this semester

    Thanks again
    METAL HEAD FOR LIFE!!!

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    Yup, wolfram is amazing. Using it in the CalcII class I am taking now.

    You can use it for just about anything you want like definitions, nutritional facts, etc.

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    Thats pretty sweet man. Calc II for me as well... gah... calculus
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    Yeah were getting into Integration and Differentation of Ln. It still shows I hate the chain rule....

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    No need for substitution, it wouldn't make the problem any easier.

    (t+3)^2= t^2+6t+9

    For simplicities sake, lets split it up.

    (t^-4)(t^2+6t+9)= t^-2+6t^-3+9t^-4

    From there it should be easy. When integrating you add one to the exponent and divide by the new exponent.

    Thus it's -t^-1-3t^-2-3t^-3
    simplified, but still overcomplicated as I'm typing on a computer lol
    -1/t((1)+(3t^-1)+(3t^-2))


    t^-3 is the same as 1/t^3, it really helps with calculus to simplify like this. Cheers.
    Last edited by owain jones; 01-07-2012 at 08:50 PM.

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