Bathroom tub leaking
The simplest thing to do is to fill the tub with water and check for leaks: 


Wait until the surrounding area is completely dry
Fill tub full of water and mark water level
Let the water stand for a couple hours
Check water level for any change and look for any signs of moisture around/under tub


On an aside, that crack looks a bit more then just cosmetic and will most likely get worse over time. If you're unable to replace the tub now, you can look for a local company that repairs fibreglass tubs. They should be able to advise you if it's repairable or not.