# Integrating factors — how in the world does one calculate those?

Is there an easier way of computing an integrating factor for differential equations? I need help understanding how to calculate those. I know the reason for them but just not familiar with how to compute exponential power functions. Help please

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Do you have some set of particular differential equations in mind? There are lots of types of integrating factors, some more obscure than others. –  mixedmath Jul 3 '11 at 6:25
For a general first-order DE of the form $f(x,y) dx + g(x,y) dy = 0$, computing an integrating factor is exactly as hard as solving the DE. Only if there happens to be an integrating factor of a special form can you hope to do it directly. –  GEdgar Jul 3 '11 at 12:31
Back from recent holiday. Well, I wanted to know if there was some easier way of generating the integration factor without needing to use exponential. :) –  user10695 Jul 6 '11 at 17:45
@user10695 The solution is what it is, we cannot change that "by methods". –  AD. Jun 29 '12 at 21:10
Since you said exponential, I'm assuming you mean first order linear? (It's the only type I know that has an exponential integrating factor). Simply take the exponential of the coefficient of the linear term. For $y'+P(x)y=Q(x)$, the integrating factor is $e^{ \int P(x)\; dx}$