Mathematica won't simplify the expression with obvious common factor of a fraction

Question

I have an expression obtain from an integral, which is:

Integrate[ϵ^2/Sqrt[(ϵ - u)^2 + Δ^2], ϵ] // FullSimplify

The denominator and numerator of the result have an obvious common factor:

Sqrt[Δ^2 + (u - ϵ)^2]

How can I let mathematica to cancel this common factor? I have tried Cancel and Refine all the variables to be positive.

Answer 1

Integrate[ϵ^2/Sqrt[(ϵ - u)^2 + Δ^2], ϵ] // Apart // FullSimplify

Answer 2

You could help Mathematica by temporarily renaming the factor.

exp = Integrate[ϵ^2/Sqrt[(ϵ - u)^2 + Δ^2], ϵ] // FullSimplify
exp /. (Δ^2 + (u - ϵ)^2) :> w
FullSimplify[%] /. w :> Δ^2 + (u - ϵ)^2