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

## Homework Statement

$$\int\frac{(5x+2)dx}{x-2}$$ from 0 to 1

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

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

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
Homework Helper
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.

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

Oops.

robphy