Integration by Partial Fractions

[cathy]

Homework Statement

1/ (x+8)(x^2+16)
Find the integral

Homework Equations

I keep getting this question wrong. Can someone check my steps?

The Attempt at a Solution

I set it up as
A/(x+8) + (Bx+C)/(x^2+16)

So I did, A(x^2+16)+ (Bx+C)(x+8)
and I did that and got
A+b=0
8B+C=0
16A+8C=1

By algebra, I solved for A, B, and C and got
A= 1/10
B= -1/10
C= 4/5

So I got 1/10ln(x+8) - 1/10∫x/(x^2+16) + 4/5∫1/(x^2+16)
and solving that out, I get 1/10ln(x+8) -1/20ln(x^2+16) + 1/5arctan(x/4)
which is not correct.
Where did I go wrong?
Thanks in advance.

 

[vela]

The linear equations A, B, and C satisfy are fine, but you didn't solve for A, B, and C correctly. If you plug in your values for A and C into the last equation, you'll see it's not satisfied.

 

[cathy]

Oh I see my mistake. Such a simple error. Thank you.