- #1
Hepth
Gold Member
- 464
- 40
$$\int dz \frac{\sqrt{\frac{1}{4} (x+1)^2 (z-1)^2-x} \log (z)}{z}$$
All values are real. The domain for z and x are both [0,1], with also the constraint that the Sqrt is real ( which means z is really from ##[0, 1-\frac{2 \sqrt{x}}{x+1}]##. I'm just trying to get the anti-derivative, and not apply the limits yet. No complex values for x or z.
I've tried many ways, and I can't seem to get it. Mathematica doesn't give a solution, and I've included the assumptions.
I think it'll be a combination of Log[z], Log[z]^2, and PolyLog[2,z] though I can't get it into a form that I can do this. Its possible due to its nature that it could be solved in terms of HyperGeometric functions too.
Does anyone have any ideas? Is there a method to solving these?
Thanks!
-Hepth
All values are real. The domain for z and x are both [0,1], with also the constraint that the Sqrt is real ( which means z is really from ##[0, 1-\frac{2 \sqrt{x}}{x+1}]##. I'm just trying to get the anti-derivative, and not apply the limits yet. No complex values for x or z.
I've tried many ways, and I can't seem to get it. Mathematica doesn't give a solution, and I've included the assumptions.
I think it'll be a combination of Log[z], Log[z]^2, and PolyLog[2,z] though I can't get it into a form that I can do this. Its possible due to its nature that it could be solved in terms of HyperGeometric functions too.
Does anyone have any ideas? Is there a method to solving these?
Thanks!
-Hepth