Solving an Integral with (3x+2)/x(x+2)^2+16x

[poopforfood]

Homework Statement

Integral of (3x+2)/x(x+2)^2+16x

Homework Equations

The Attempt at a Solution

That breaks down to

A/x + Bx+c/x^2+4x+20

so 3x+2 = Ax^2+4x+20 + Bx^2 + Cx

then I found the values of A b and C then I can't figure out what to do please help

 

[Kreizhn]

What did you get for values of a,b,c?

And by the way, is that supposed to be

$$\frac{3x+2}{x(x+2)^2+16x}$$?

because the way it's written is

$$\frac{3x+2}{x} (x+2)^2 + 16x$$

 

[poopforfood]

yea that's what its suposed to be

 

[Kreizhn]

And did you by chance get A= 1/10, B = -1/10, C= 26/10?

 

[poopforfood]

yeaup

 

[poopforfood]

I don't know what to do after this

 

[Kreizhn]

well, the $\frac{1}{x}$ is pretty easy to handle right? So we'll just focus on the other term. Now, in this case it's better if we express $x^2+4x+20$ as $(x+2)^2+16$.

Make the substitution $x+2 = 4 \tan(\theta)$ and don't forget that in this case [itex] dx = 4 \sec^2(\theta) d\theta [/tex]. Substitute everything into your integral and see if it simplifies a bit.

 

[poopforfood]

I don't know what to do after this

 

[Kreizhn]

If you do what I've said to do, and you do it correctly, your integral will become much easier, so just stick with it.

 

[poopforfood]

I don't know what to do after this

 

[Kreizhn]

Well why don't you show me what you've got so far and we'll see if we can't see where the problem is, because if you done it correctly the integral is blatantly obvious.