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

1. Dec 8, 2007

### erjkism

i am trying to integrate Integrate (5x+2)dx/(x-2) from 0 to 1. i have tried splitting the equation up into (5x)/(x-2) + (2)/(x-2)
i have tried every U substitution i can think of but i cant figure out how to do it.

2. Dec 8, 2007

### cristo

Staff Emeritus
Which substitutions have you tried? What about u=x-2?

Note in future that you should post these sort of questions in the suitable homework forum, and no the technical forums.

3. Dec 8, 2007

4. Dec 8, 2007

### ice109

integration by parts

u=(5x+2) dv=(1/(x-2))

how would that work?

Last edited: Dec 8, 2007
5. Dec 8, 2007

The u substitution suggested above completely kills the problem ice. The integral becomes a linear polynomial in u over u, and then can be broken into pieces and integrated by the power rule.

6. Dec 8, 2007

### cristo

Staff Emeritus
Let u=x-2, then du=dx and x=u+2. This converts the integral into $$\int\frac{5(u+2)du}{u}=\int\left[5+\frac{10}{u}\right]du$$

7. Dec 8, 2007

feck im dumb