Integration using u substitution and arctan

[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 derivative of the bottom and that the other top is the right constant.

 

[Pere Callahan]

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

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

 

[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

 

[Pere Callahan]

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

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