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.
Click on it twice and it will be large and clear. It is obtained using the Wolfram Mathematica Online Integrator
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)
=(x^4-1)(x+1)
I just don't understand how the book got that.
How does this factorisation relate to your posted question? The final line is got by taking out the common factor of (x+1).
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.