Question

Why we don't add constant of integration in integrating factor?

Answer 1

In calculus, the indefinite integral of a given function (i.e., the set of all antiderivatives of the function) on a connected domain is only defined up to an additive constant, the constant of integration. This constant expresses an ambiguity inherent in the construction of antiderivatives.

Answer 2

So you're multiplying both sides of the differential equation by
e∫p(x)dx

Assume that ∫p(x)dx=P(x)+C∫p(x)dx=P(x)+C,
so

e∫p(x)dx=eP(x)+C=eC∗eP(x)

So, you multiply both sides of the equation by this integrating factor, only to find you can just divide off the constant eC again. Thus, we skip that step and just ignore the constant.

where eC means e to the power C

Thanks.