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what does a integrating factor tells about a differential equation?

in order to find the solution for a exact equation we multiply the equation by integrating factor(I.F).

as intergrating factor=e^integration(p)dx

i.e given by I.F=e^gx where gx is integration of p

now as we have integrated the p we did not add any constant to the integration which is gx.

may i know the reason why we did not add any constant over there.

advanced thanks