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

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.

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.

integration by parts

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

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.
how would that work?

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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.

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