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Math Help - Another stuborn integral

  1. #1
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    Another stuborn integral

    \int\frac{3x^2-7x+2}{2x+4}

    I really do not even know where to start. I am very rusty, I took calculus 1 three years ago, and I am now taking calculus 2.
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by gammaman View Post
    \int\frac{3x^2-7x+2}{2x+4}

    I really do not even know where to start. I am very rusty, I took calculus 1 three years ago, and I am now taking calculus 2.
    To start this off you will need to do polynomial long division, since the degree of the numerator is larger than the degree of the numerator. Then use partial fractions. Does that help you get started?
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  3. #3
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    Not really, like I said it has been a long time, and I have forgot many of the basic "rules", show me as if I am retarded, you will not insult me.
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  4. #4
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    Quote Originally Posted by gammaman View Post
    Not really, like I said it has been a long time, and I have forgot many of the basic "rules", show me as if I am retarded, you will not insult me.
    This is not a calculus rule, it is merely algebra.

    \frac{3x^2 -7x + 2}{2x + 4} = \frac{3}{2} x - \frac{13}{2} + \frac{28}{2x + 4} = \frac{3}{2} x - \frac{13}{2} + \frac{14}{x + 2} .

    Read this: Polynomial Long Division
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  5. #5
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by gammaman View Post
    Not really, like I said it has been a long time, and I have forgot many of the basic "rules", show me as if I am retarded, you will not insult me.
    LOL! If you are taking Calc II you are more than likely not retarded. When you don't use Calculus on an almost daily basis, you quickly forget the techniques. You should really go through and refresh yourself on these techniques.

    Ok, so polynomial long division, use need it to make the degree of the polynom. in the numerator smaller than the one in denominator.

    \int \frac{3x^2-7x+2}{2x+4} dx

    2x + 4 |\overline{3x^2 - 7x +2}

    **See here for the long division steps, can't make it work on here
    Long division polynomial.doc

    The numbers in red on the attachment are the numbers you use in your new integral:

    Original problem: \int \frac{3x^2-7x+2}{2x+4} dx

    New integral: = \int \frac{3}{2}x - 6 + \frac{28}{2x+4} dx

    I was wrong about needing partial fractions for this one. You can just integrate it normally. Some long division polynomial problems you will want to combine your answers into a new rational integral with a smaller polynomial in the numerator and then use partial fractions.

    *Sorry this took me so long to get to you!
    Let me know if you still need help!
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  6. #6
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    Quote Originally Posted by mollymcf2009 View Post
    New integral: = \int \frac{3}{2}x - 6 + \frac{28}{2x+4} dx
    Sorry to be a bother, but how would I solve this new integral?
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  7. #7
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by gammaman View Post
    Sorry to be a bother, but how would I solve this new integral?
    You remember how to take antiderivatives, right?

    Here is a simple integral just to remind you:

    \int 2x^2 - \frac{1}{x-2} dx

    = \frac{2}{3}x^3 - ln|x-2|

    So for this one:

    \int \frac{3}{2}x - 6 + \frac{28}{2x+4} dx

    = \frac{3}{2} \cdot\frac{x^2}{2} - 6x + 28(ln|2x+4|) + C

    = \frac{3x^2}{4} - 6x + 28ln|2x+4| + C

    Got it now?
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  8. #8
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    That helps. By the way, is there a particular integration method that works for all integrals.
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  9. #9
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    Quote Originally Posted by gammaman View Post
    That helps. By the way, is there a particular integration method that works for all integrals.
    Unfortunately, no.

    There are many techniques - recognising which one to try for a given problem is the trick. Experience - the consequence of extensive practice - is what's usually required.
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  10. #10
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    Could this problem be done using integration by parts? I find myself becoming fond of that method.
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  11. #11
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    integration by parts is normally used for integrating a product of two functions.

    the last integral posted by mollymcf2009 is straight forward, term-for-term integration.
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