1
$\begingroup$

I have an integration with assumptions and limits of integration. I tried to use Mathematica to solve this problem, but I cannot get any results.

Integrate[1/(w^4 + 2 (2 ξ^2 - 1) w^2 ω1^2 + ω1^4), {ω1, 0, t}, 
  Assumptions -> {w > 0, 1 > ξ > 0}]]

What should I do?

$\endgroup$
3
  • $\begingroup$ Welcome to Mathematica.SE! I suggest that: 1) You take the introductory Tour now! 2) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! 3) As you receive help, try to give it too, by answering questions in your area of expertise. $\endgroup$
    – bbgodfrey
    Commented Mar 7, 2015 at 1:58
  • 1
    $\begingroup$ This could be considered a duplicate of How to do symbolic definite integral without copy and paste the intermediate results? $\endgroup$
    – Jens
    Commented Mar 7, 2015 at 4:54
  • $\begingroup$ I agree with @Jens. All those definite integrals that can be solved by doing the indefinite one should be "the same" question, lest we are going to repeat the trick over and over $\endgroup$ Commented Mar 7, 2015 at 15:14

1 Answer 1

2
$\begingroup$

Evaluating the indefinite integral works better.

sol = Integrate[1/(w^4 + 2 (2 v^2 - 1) w^2 w1^2 + w1^4), w1, Assumptions -> {w > 0, 1 > v > 0}]

(* (-(ArcTan[w1/(Sqrt[-1 + 2*v^2 + 2*v*Sqrt[-1 + v^2]]*w)]/
   Sqrt[-1 + 2*v^2 + 2*v*Sqrt[-1 + v^2]]) - 
   ArcTanh[w1/(Sqrt[1 - 2*v^2 + 2*v*Sqrt[-1 + v^2]]*w)]/
   Sqrt[1 - 2*v^2 + 2*v*Sqrt[-1 + v^2]])/(4*v*Sqrt[-1 + v^2]*w^3) *)

If the limits of integration are important, then evaluate

sol/.w1 -> t - sol/.w1 -> 0

(The second term, incidently, is 0.)

$\endgroup$
4
  • $\begingroup$ @Nasser I don't see anything wrong with this answer. Just different letters. $\endgroup$
    – Jens
    Commented Mar 7, 2015 at 4:53
  • $\begingroup$ @Jens oh sorry, I saw 2 w's in there. did not notice one had 1 stuck to it. $\endgroup$
    – Nasser
    Commented Mar 7, 2015 at 5:10
  • $\begingroup$ Actually I want the final limits, w1->infinity-w1->0, and the assumption 1>v>0.@bbgodfrey $\endgroup$
    – whdwpy666
    Commented Mar 9, 2015 at 1:46
  • $\begingroup$ @whdwpy666 The limits you request were not part of your Question but can applied easily to obtain, (Pi*(Sqrt[-(1/((1 - 2*v^2 + 2*v*Sqrt[-1 + v^2])*w^2))] - Sqrt[1/((-1 + 2*v^2 + 2*v*Sqrt[-1 + v^2])*w^2)]))/(8*v*Sqrt[-1 + v^2]*w^2) The assumption 1>v>0 was used to obtain the answer, as requested. $\endgroup$
    – bbgodfrey
    Commented Mar 9, 2015 at 2:16

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