How Do You Solve This Complex Partial Fraction Integration?

[bayan]

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 science 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?

 

[Nylex]

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?

 

[whozum]

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.

 

[Gale]

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.

 

[whozum]

Fine Gale, take the kill.

 

[bayan]

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?

 

[Gale]

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.

 

[whozum]

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.

 

[bayan]

Thanx guys.