Hi, while solving differential equations problems we have to sometimes use absolute value while taking an integral of which 1 over a function. But in some problems I understand that we do not have to use absolute value sign for example if the function related with atom number which can never be a negative number we do not have to use absolute value. But in the picture I added here there is no sign about physical meaning of the problem so I think we should use absolute value and so there should have to be two different answers. The second picture of handwritting is my other solution. The last one is a topic related with the problems. Have a nice day.