Determining state of charge using current sensor (ACS758) with arduino uno
Instead of using a separated component for each thing you can use a proper solution that is itself already a combination of both: the DS2438's integrated current accumulator. This link explain it pretty well, also here is a library to use it with arduino. They are pretty cheap (a few dollars) and will perform very well!

Although, in your place I would consider choosing a different approach. I don't know which kind of battery (Li-ion, LiPo, Lead-acid..) you are using, but in many cases if you monitor the battery voltage, you can have enough information about the battery state. I can't ask you in comment yet beause I'm new here and don't have enough reputation, but if you can describe better the kind of battery you are using and what you intend to monitor which your circuit, I can edit this post to offer you a better solution.