Integration of Rational Functions with Partial Fractions

[alexis36]

Homework Statement

Integration of 1/(x^2-5x+6)

Homework Equations

The Attempt at a Solution

I know i cannot do ln|x^2-5x+6|
I've tried some form of substitution or intergration by parts, and they don't work.
Should I factor the bottom?

 

[jhicks]

Have you tried partial fractions, as the title suggests? To be brief, you can rewrite $$\frac{1}{x^2-5x+6}$$ as $$\frac{a}{x-2}+\frac{b}{x-3}$$ where you must find a and b.

 

[alexis36]

Okay.. I've solved the question up to a certain point. (I've decided that it's do-able without partial practions..)
however; now I am stuck on an integration:
i might find the integral of
1/(x^2-5x+6)
and now I am not sure if i use substituion, integration by parts, or bring the bottom up to the top of the fraction for this integration?

 

[rocomath]

I've solved the question up to a certain point. (I've decided that it's do-able without partial practions..)

Ok, show us then. Maybe we can help you from there.

 

[alexis36]

So partial fractions is the way to go I think..
I have
A/(x-3) + B/(x-2) = )A(x-2)+B(x-3))/(x-2)(x-3)
Ive solved for A and B and I got 1 for each of them.
Now I need to go and integrate 1/(x-2) and 1/(x-3) right? and set that equal to (t+c) and then solve the autonomous equation as i would any?

 

[rocomath]

Now I need to go and integrate 1/(x-2) and 1/(x-3) right?

Yes, you would integrate it from here.

 

[Dick]

A=1 and B=1 doesn't work. Think about the signs again.