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

erjkism

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?

Dick

Yep, the obvious one. u=x-2. dx=du. x=2+u.

robphy

Another way to split it up [without explicitly invoking a substitution]
is to write the numerator 5x+2 as 5(x-2)+12.

rocomath

Woah, woulda never thought of that. Nice, I want your vision :-]

Dick

You'll still want u=x-2 to do the 12/(x-2) part.

Mystic998

Just do polynomial division. It becomes 5 + 12/(x - 2).

Oops.

robphy

True... and now the substitution is really obvious.