4
$\begingroup$

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.

$\endgroup$
6
$\begingroup$
Integrate[ϵ^2/Sqrt[(ϵ - u)^2 + Δ^2], ϵ] // Apart // FullSimplify
$\endgroup$
3
$\begingroup$

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

Mathematica graphics

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.