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Math Help - Simple Calc Question

  1. #1
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    Simple Calc Question

    I am entering Calc 2, and trying to evaluate this integral WITHOUT knowledge of more advanced integration techniques. Only using u-substitution and integral techniques covered in Calculus I, is it possible to evaluate this? I was under the impression that u-substituion is only applicable in neat little situations where the derivative of the substituted equation is in some way made equivalent to what isn't being substituted (i.e. their powers are equal).

    (2x+1)/x3

    u= x^3
    du = 3x^2 dx
    ???????
    Last edited by terminus1256; September 2nd 2014 at 09:38 AM.
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  2. #2
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    Re: Simple Calc Question

    no substitution necessary ... just straightforward algebra.

    \int \frac{2x+1}{x^3} \, dx = \int \frac{2x}{x^3} + \frac{1}{x^3} \, dx = \int \frac{2}{x^2} + \frac{1}{x^3} \, dx = -\frac{2}{x} - \frac{1}{2x^2} + C
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  3. #3
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    Re: Simple Calc Question

    Oh god, that is so simple. I feel like a dunce! Thanks.
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