Antidifferentiation for a larger problem

1. The problem statement, all variables and given/known data
I'm trying to antidifferentiate a function in order to find the volume of a solid. The function comes out to be (2x+1)/(x^2+8x+16)


2. Relevant equations

N/A

3. The attempt at a solution
I've tried a multitude of things. I figured that partial fractions would work, but it turns out that since the denominator is a square that doesn't work. I'm not asking you to solve, just a nudge in the right direction

 

ALright. I don't understand though. Where did the third (x+4) come from. The denominator only factors to (x+4)(x+4)

 

Okay even when i try that I get

A(x+4)^2+B(x+4) = 2x+1

When I plug in to eliminate one of the variables (x=-4) then I get 0+0 = -7. I'm probably doing something wrong.

 

Ok. I'll try that. Why did you use those denominators though, for the partials. Intuitively I would use x+4 and x+4 because they multiply together to get x^2 +8x+16

Thanks though

 

Alright. So I solve that equation and get 2x+1 = A(x+4) + B

A = 1 and B = -7

WHen I antidifferentiate I get ln(x+4) + 7/(x+4) Seems that I'm missing a factor of 2 in front of the first term. Sorry for the problems.

 

nevermind on that last part, i found a mistake. but the previous question is still troubling me

 

Alright that makes sense. I'm trying to solve that equation now. I can solve for B=-7, but I can't solve for A because I have two variables: x and A.

 

Oh nvm. I got it. I have the problem solved now. I really appreciate the help cristo, you've enhanced my understanding of partial fractions.