Sure, although it s usually called a receipt, not an invoice. Any taxi will give you a receipt, just ask.
Some cab companies furnish them, some don t. And since you are travelling to different places, it would difficult to determine that. Could you have them sign a voucher from your company? Some cabbies may not want to do that since they are probably skimming and wouldn t want to sign anything. You can only ask and explain why you need it. I m sure most of them have a way of getting you a receipt.