# Thread: Help!!!! Integration!!

1. ## Help!!!! Integration!!

Hi! I am integrating (1) over (x^2+4x-32) and I know that that can be separated into the integral of (A) over (x-4) plus the integral of (B) over (x+8) but I don't know how to solve for A and B. I have 1= A(x+8) + B(x-4). So 1=Ax+A8+Bx+-B4. All I know is that (A+B)x, A+B=0 since there are no x variables. Just 1. Please help me figure out the values for A and B!!! It's probably easy I just am not figuring it out! Thanks!!

2. Hello
Originally Posted by elocin
Hi! I am integrating (1) over (x^2+4x-32) and I know that that can be separated into the integral of (A) over (x-4) plus the integral of (B) over (x+8) but I don't know how to solve for A and B. I have 1= A(x+8) + B(x-4). So 1=Ax+A8+Bx+-B4. All I know is that (A+B)x, A+B=0 since there are no x variables. Just 1. Please help me figure out the values for A and B!!!
You're right, there is no $\displaystyle x$ at the numerator so $\displaystyle A+B=0$. What you forgot is that the numerator of $\displaystyle \frac{1}{x^2+4x-32}$ is 1 () so we also have $\displaystyle 8A-4B=1$.

3. Hmm. Yes I think I knew that, but how do you solve for that? A and B have to be equal but opposite signs, so I don't know how to solve for it. I tried plugging in numbers, but I'm not getting anywhere!

4. Never mind, it's 1/12!! Thanks!