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

by erjkism
Tags: 2dx or x2, integrate
 P: 54 1. The problem statement, all variables and given/known data $$\int\frac{(5x+2)dx}{x-2}$$ 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?
 Sci Advisor HW Helper Thanks P: 25,235 Yep, the obvious one. u=x-2. dx=du. x=2+u.
 Sci Advisor HW Helper PF Gold P: 4,139 Another way to split it up [without explicitly invoking a substitution] is to write the numerator 5x+2 as 5(x-2)+12.
P: 1,754
Integrate (5x+2)dx/(x-2) from 0 to 1

 Quote by robphy 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 :-]
HW Helper
Thanks
P: 25,235
 Quote by robphy 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.
 P: 206 Just do polynomial division. It becomes 5 + 12/(x - 2). Oops.