I'm searching for the meaning of "Up to"
It means that in the sum of terms on the right side of the equation, one is ignoring all powers of x higher than 1. In general, these higher powers may or may not be integers. Ignoring these higher powers becomes a better and better approximation to the left-hand side of the equation the smaller x becomes. To define it precisely, you need to use mathematical limits. @ColinFine is correct. You won't find this in general English dictionaries.