The order of integration was given to be that way too. I tried splitting the denominator and using partial fractions, but I could not find a way to split it since. Since the 1 is at the end, and the beginning, the only option are (z-1)(z+1)(-z+1)(-z-1) With that, there isn't a way to get 48z. In addition, the z^2 factors must get rid of each other.
It can't be beyond the scope of the course. It has to be solvable. Only thing is I can't see a way to change it to cylindrical or spherical, and I don't see a way to factor the polynomial into multiples. What I was looking at was this example.
x^5 + x^4 - x -1 = x^4(x+1)-(x+1)
I just don't understand how the book got that.
Re: Your original question. Is there a typo in the book? The cubic has no simple factors. For the final time: Go and ask whoever gave you the question how s/he expects you to solve it.
I tried some new things. First I tried changing the order of integration. No luck there, because two of the limits contain variables. This makes dzdydz, the only order of integration.
Looks at the denominator, I turned it into
-z(z^2 - 48) + 1 which then turns into
-z(z+7)(z-7) + (1-z) This is still equal, and almost able to use partial fractions, I just don't see a way to get rid of the 1-z and move it as a factor into the others. I still think that partial fractions must be the way, but there is something I'm not seeing.
I plugged values in yours while comparing it to the third degree polynomial and the equality doesn't exist. I also looked around for a quadratic formula similar to the one used for second degree equations and there isn't anything we haven't learned in school yet. They're all very complex formulas. I am downloading mathmatica to see if it does me any good. I tried another program and it couldn't even solve it.