The description for MUL r/m32 is Unsigned multiply (EDX:EAX <- EAX * r/m32)..
That means that the 64-bit product will be stored in EDX:EAX, i.e. the upper 32 bits ends up in EDX and the lower 32 bits in EAX. Which fits with the results you're seeing, since the product should be 0x1DBEE41EB22A9CB.