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

[erjkism]

Homework Statement

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

Homework Equations

The Attempt at a Solution

I've tried splitting it up into (5x)/(x-2) + (2)/x-2), but i couldn't go any farter. Ived also tried using lots of U subsitutions, but i can't 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]

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]

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]

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

Oops.

 

[robphy]

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

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