With almost every white shirt, sweat stains are an annoyance that is practically inevitable. But sometimes there isn't time to do another load of laundry, or it isn't cost-efficient or good for the environment to wash a single shirt over a sweat stain. There are plenty of ways to remove sweat stains from the underarms of shirts without washing for those times when the washing machine isn't an option.
Dry your white shirts in the sun. Drying them in the sun can help whiten your shirts even after they're already washed. Drying them in the heat of the dryer can set stains and make them much harder to get out.
Treat the stain with bleach. If the stain is still fresh, then you may be able to remove it with a bleach pen. Simply liberally apply the pen to the affected area and leave it alone for a few minutes. Dab the stain and bleach with a paper towel and the stain should be gone. Using a bleach pen will work a lot better if you do wash the clothes after application, but it should be able to get light stains out even without doing a load of laundry. You can also use a bleach pen to prevent stains if you know you might cause them with a lot of sweating. Just apply after whatever activity you think will bring about the stains, before you actually see them. Then follow the other directions as normal.
Dip the shirt in aspirin. Two tablets of aspirin in about half a cup of water will draw any sweat stains from shirts without washing them, although as with the bleach pen, this will be much more effective if you wash the clothes afterward.
Spray with a homemade detergent solution. Mix laundry detergent with water, with only about a quarter as much water as detergent, and put this solution in a spray bottle. Spray the shirt around the area of the stain and scrub with any spare brush you have; a spare toothbrush works well.
Use baby wipes. Wiping the stain gently with baby wipes can often bring the stain out. It works because of the alcohol in the baby wipes, but don't use too much of any kind of alcohol. The lingering smell can be a bit strong.