Integration using u substitution and arctan

1. Mar 25, 2008

dante3001

so i'm having problems with the coefficients in this problem.

$$\int$$(10z+8/z^2-8z+41)dz

i know that the main chunk is

(a)ln|(z-4)^2+25|+(b)arctan((z-4)/5)

a and b are 5 and 32/5 respectively
the problem is i can't seem to split up the top so that the first portion is the derivitive of the bottom and that the other top is the right constant.

2. Mar 25, 2008

Pere Callahan

If this is not the answer how it is related to the question..?

3. Mar 25, 2008

dante3001

the main part is not what i need explained which is the chunk there. it is the a and b portion. i just need to know how the coefficients are found

4. Mar 25, 2008

Pere Callahan

Do you mean
$$\int\frac{10z+8}{z^2-8z+41}dz$$
?

To me it is not clear what you already solved and where your problem is. I suggest you present what you did so far and how you obtained the partial answer (a).

-Pere

Last edited: Mar 25, 2008