# Partial fraction Urgent

Hi every one.

Just came acroos a nasty piece and was wondering if you could help me with it.

I wasn't sure if it belong to math section or here but scince it is for my homework I placed it here.
Here is the question.
Find the integral of $$\frac{x}{(x+1)(x-2)^2}$$
I have gotten to some piont using the partial fraction.
here is my work so far.

$$\frac{A}{(x+1)}+\frac{B}{(x-2)}+\frac{C}{(x-2)^2}$$

I found the values of A B and C.

C=$$\frac{2}{3}$$ B=$$\frac{2}{3}$$ A=$$\frac{21}{9}$$

If you could be so kind and help me through with it by typing what you have done would be really nice, I am not asking in latex form a simple typing will do the job.

Also can anyone help me finding the equation of the graph attached?

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bayan said:
If you could be so kind and help me through with it by typing what you have done would be really nice, I am not asking in latex form a simple typing will do the job.
No-one is going to do your work for you. You've done the partial fractions, so what's wrong with doing the integration?

If you've found A B and C ccorrectly (havent checked yet) then you can just substitue your new expression into hte integral.

$$\int \frac{x}{(x+1)(x-2)^2} dx = \int \left(\frac{2}{3(x+1)} + \frac{2}{3(x-2)} + \frac{7}{3(x-2)}\right) dx$$ which are all trivial integrals.

If those are correct values for A B and C it simplifies even more.

your partial fractions is wrong. i get this system

A+B=0
-4A-B+C=1
4A-2B+C=0

then solve for a b and c again. then plug them in and replace your initial integral with your partial fractions. shouldn't be too bad from there. show your work if you're still stuck.

Fine Gale, take the kill.

Let me first check if I have it right.

To get partial fraction I would need 3 definitions, right?

Like

$$\frac{A}{x+1} + \frac{B}{x-2} + \frac{C}{(x-2)^2}$$.

Then solve for A,B and C.

then do the integration.

In my last attempt I ended up with a $$Ln$$ and a function.

Is it sposed to be like that?

Any help with the graph?

you should end up with two Ln functions and a rational function after the integration. plus don't forget an integrating constant.

The graph hasn't been approved yet, so can't help you till we see it.

Thats the correct equation, equate it to the original integrand and multiply out by the denominator, and solve the resulting system of equations for A B and C. Once you get those, itnegrate the equivalent partial fractions, each one will evaluate to a LN of a function except the last one.

Thanx guys.