Integrating Factor: -g(m/g) and its Derivative

[Ry122]

In the following problem how does -g end up becoming -g(m/g)?
Isn't the derivative of -g just (-g^2/2)?
http://users.on.net/~rohanlal/integfact.jpg

 

[Wretchosoft]

I'm having trouble reading the scan, but from what I can tell, the factor of (m/c?) came from integrating the exponential, and g is constant with respect to the variable t. Then again, I don't have any context either.

 

[Chaos2009]

Yes, in this case g is a constant because you are integrating with respect to t. If you were integrating with respect to g (no clue why you would because I strongly suspect that this is the gravitational constant) then everything else would be a constant and you would get -g^2/2.

 

[Ry122]

Shouldn't I also have to find the integral of g, which would be gt?