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

1. ### erjkism

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?

2. ### Dick

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

3. ### robphy

4,394
Another way to split it up [without explicitly invoking a substitution]
is to write the numerator 5x+2 as 5(x-2)+12.

4. ### rocomath

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

5. ### Dick

25,853
You'll still want u=x-2 to do the 12/(x-2) part.

6. ### Mystic998

206
Just do polynomial division. It becomes 5 + 12/(x - 2).

Oops.

7. ### robphy

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

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