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

  • Thread starter erjkism
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  • #1
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Homework Statement



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


Homework Equations



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?
 

Answers and Replies

  • #2
Dick
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Yep, the obvious one. u=x-2. dx=du. x=2+u.
 
  • #3
robphy
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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.
 
  • #4
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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.
Woah, woulda never thought of that. Nice, I want your vision :-]
 
  • #5
Dick
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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.
You'll still want u=x-2 to do the 12/(x-2) part.
 
  • #6
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Just do polynomial division. It becomes 5 + 12/(x - 2).

Oops.
 
  • #7
robphy
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You'll still want u=x-2 to do the 12/(x-2) part.
True... and now the substitution is really obvious.
 

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