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Math Help - Evaluating an integral

  1. #1
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    Evaluating an integral

    \int_{1}^{3} \frac{dx}{x(x+1)^2}

    I can't seem to come across a solution, any ideas?
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  2. #2
    MHF Contributor matheagle's Avatar
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    partial fractions

     \frac{1}{x(x+1)^2}= { a\over x}+{ b\over x+1}+{ c\over (x+1)^2}
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  3. #3
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    I'm sorry, I should have been more clear, but I just recently "learned" how to do these type of problem. I haven't really been able to apply it though. Could you please help me through with a step by step sort of approach?
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  4. #4
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    Quote Originally Posted by looseenz2 View Post
    I'm sorry, I should have been more clear, but I just recently "learned" how to do these type of problem. I haven't really been able to apply it though. Could you please help me through with a step by step sort of approach?
    Partial-Fraction Decomposition: General Techniques
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  5. #5
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    this is how you avoid partial fractions to save time:

    put x=\frac1t and the integral becomes \int_{\frac13}^1\frac t{(t+1)^2}\,dt now substitute u=t+1 and the integral becomes \int_{\frac43}^2\frac{u-1}{u^2}\,du, thus the rest should be pretty easy.
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  6. #6
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    I have tried to learn it through various websites, it's just hard for me to grasp for some reason, but thanks anyway
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