Bernoulli equations

It is a first order ODE in the form

u_{1} + p (x) u = q (x) u^{n}

where $p, q$ are functions of $x$ and $n \in N$ .

They are solved by a substitution $v = u^{1 - n}$ to convert it in a linear ODE, which we always know a integrating factor for.
Ver esta web.

But I have proof that we can solve it directly with the integrating factor

μ = - \frac{e^{\int (1 - n) p (x) d x}}{u^{n}}

ver [Maple 013].