Consider the following integral where $s,r,b \in \mathbb{R}_{>0}$ are constants and $x,y,z\in \mathbb{R}$ are independent variables
$$I = \iiint \frac{1}{s \left(- x + y\right) \left(- b z + x y\right) \left(x \left(r - z\right) - y\right)}\, dx\, dy\, dz.$$
I have tried partial fractions, a few different U substitutions, and integration by parts without success.
A Integral Calculator completes integrating with respect to $x$, giving the expression
$$I = \iint \dfrac{\left(z-r\right)\left(bz-y^2\right)\ln\left(\left|\left(z-r\right)x+y\right|\right)+y^2\cdot\left(z-r+1\right)\ln\left(\left|yx-bz\right|\right)+\left(-bz\cdot\left(z-r\right)-y^2\right)\ln\left(\left|x-y\right|\right)}{sy\cdot\left(z-r+1\right)\left(bz-y^2\right)\left(bz\cdot\left(z-r\right)+y^2\right)}\ dy\ dz$$
but it refuses to integrate further.
Quation
How can I complete evaluating the integral either into a closed form or a special function?
Wolfram Alpha gave me
(2 Log[x - y] Log[y] - 2 Log[y] Log[1 - y/x] - Log[x - y] Log[1 + (-x + y)/(x - Sqrt[b] Sqrt[z])] - Log[x - y] Log[1 + (-x + y)/(x + Sqrt[b] Sqrt[z])] + Log[(x + (x y)/(Sqrt[b] Sqrt[z]))/(x + Sqrt[b] Sqrt[z])] Log[x y - b z] - 2 Log[y] Log[-(r x) + y + x z] + Log[x y - b z] Log[1 + (-(x y) + b z)/(Sqrt[b] x Sqrt[z] - b z)] - Log[x y - b z] Log[1 + (-(x y) + b z)/(Sqrt[b] x Sqrt[r - z] Sqrt[z] - b z)] - Log[x y - b z] Log[1 + (x y - b z)/(Sqrt[b] x Sqrt[r - z] Sqrt[z] + b z)] + 2 Log[y] Log[1 + y/(-(r x) + x z)] + Log[-(r x) + y + x z] Log[1 + (-(r x) + y + x z)/(r x - Sqrt[b] Sqrt[r - z] Sqrt[z] - x z)] + Log[-(r x) + y + x z] Log[1 + (-(r x) + y + x z)/(r x + Sqrt[b] Sqrt[r - z] Sqrt[z] - x z)] - 2 PolyLog[2, y/x] - PolyLog[2, (x - y)/(x - Sqrt[b] Sqrt[z])] - PolyLog[2, (x - y)/(x + Sqrt[b] Sqrt[z])] + PolyLog[2, (x y - b z)/(Sqrt[b] x Sqrt[z] - b z)] - PolyLog[2, (x y - b z)/(Sqrt[b] x Sqrt[r - z] Sqrt[z] - b z)] + PolyLog[2, (-(x y) + b z)/(Sqrt[b] x Sqrt[z] + b z)] - PolyLog[2, (-(x y) + b z)/(Sqrt[b] x Sqrt[r - z] Sqrt[z] + b z)] + 2 PolyLog[2, y/(r x - x z)] + PolyLog[2, (-(r x) + y + x z)/(-(r x) - Sqrt[b] Sqrt[r - z] Sqrt[z] + x z)] + PolyLog[2, (-(r x) + y + x z)/(-(r x) + Sqrt[b] Sqrt[r - z] Sqrt[z] + x z)])/(2 b s (-1 + r - z) z)
as the output to integrating with respect to $x$ and then $y$ assuming a complex logarithm. Here is an image of the output of this second integration:
This expression would be the remaining integrand for $dz$. Unfortunately I have exceeded the maximum character input for Wolfram alpha beyond that.