Integrate (5x+2)dx/(x-2) from 0 to 1

  1. 1. The problem statement, all variables and given/known data

    [tex]\int\frac{(5x+2)dx}{x-2}[/tex] from 0 to 1


    2. Relevant equations

    3. The attempt at a solution

    ive tried splitting it up into (5x)/(x-2) + (2)/x-2), but i couldnt go any farter. Ived also tried using lots of U subsitutions, but i cant figure out what do next. Is there some trick that i am not seeing?
     
  2. jcsd
  3. Dick

    Dick 25,853
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    Yep, the obvious one. u=x-2. dx=du. x=2+u.
     
  4. robphy

    robphy 4,394
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    Another way to split it up [without explicitly invoking a substitution]
    is to write the numerator 5x+2 as 5(x-2)+12.
     
  5. Woah, woulda never thought of that. Nice, I want your vision :-]
     
  6. Dick

    Dick 25,853
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    You'll still want u=x-2 to do the 12/(x-2) part.
     
  7. Just do polynomial division. It becomes 5 + 12/(x - 2).

    Oops.
     
  8. robphy

    robphy 4,394
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    True... and now the substitution is really obvious.
     
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