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

by erjkism
Tags: 2dx or x2, integrate
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erjkism
#1
Dec8-07, 07:14 PM
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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?
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Dick
#2
Dec8-07, 07:15 PM
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Yep, the obvious one. u=x-2. dx=du. x=2+u.
robphy
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Dec8-07, 07:22 PM
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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.

rocomath
#4
Dec8-07, 07:28 PM
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Integrate (5x+2)dx/(x-2) from 0 to 1

Quote Quote by robphy View Post
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 :-]
Dick
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Dec8-07, 07:38 PM
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Quote Quote by robphy View Post
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.
Mystic998
#6
Dec8-07, 08:00 PM
P: 206
Just do polynomial division. It becomes 5 + 12/(x - 2).

Oops.
robphy
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Dec8-07, 08:08 PM
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Quote Quote by Dick View Post
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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