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Integration problem in terms of reals returns complex result

Posted 3 years ago

How can I get an answer in real terms?

$Assumptions = (x|y|z|a|b|c)\[Element] Reals

p:=Sqrt[(a-x)^2+(b-y)^2+(c-z)^2]

I1a= Integrate[a/p,b]//FullSimplify

I2a =Integrate[I1a,c]//FullSimplify
POSTED BY: Renata Litovzeva
2 Replies

This combination gives a real expression:

Simplify[ComplexExpand@Simplify[I2a // TrigToExp,
    {a > x, b > y, c > z}] /.

  Arg[u_] :> ArcTan[ComplexExpand[Im[u]/Re[u]]]]
POSTED BY: Gianluca Gorni

Thank you. It works really well.

POSTED BY: Renata Litovzeva
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