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I have a triple integral which is kind of complex, and I want to use Mathematics to help me do the integral. However, when I press "Enter" and "Shift" the software get stuck. I wonder whether this integral cannot be compute?enter image description here

f[x_]:=1/(A-F*x^2+x*B I); g[y_]:=1/(A-F*y^2+y*B I); h[z_]:=1/(A-F*z^2+z*B I); j[x_,y_,z_]:=1/(A-F*(x+y+z)^2-(x+y+z)*B I); result=Integrate[f[x_]*g[y_]*h[z_]*j[x_,y_,z_],x_,y_,z_]
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    $\begingroup$ Your figure is illegible. Please post copyable code. $\endgroup$ Commented Mar 13, 2015 at 1:39
  • $\begingroup$ you should not have the underscores in the last expression $\endgroup$ Commented Mar 13, 2015 at 3:14

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Your integral is too complicated for closed form. After fixing your syntax error, and integrating w.r.t. x only, you can see the result contains complex value and very complicated trig functions. Mathematica can't do the integration w.r.t. y at this stage

f[x_] := 1/(a - c*x^2 + x*b I); g[y_] := 1/(a - c*y^2 + y*b I); h[z_] := 1/(a - c*z^2 + z*b I); j[x_, y_, z_] := 1/(a - c*(x + y + z)^2 - (x + y + z)*b I); result = Integrate[f[x]*g[y]*h[z]*j[x, y, z], x]

Mathematica graphics

Integrate[result, y] (*wait....wait...*)

Mathematica graphics

Do you think there is closed form solution for this? Have you considered numerical integration?

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  • $\begingroup$ I learnt this from an article that is Non‐Normal Stochastic Response of Linear Systems. This article wants the result as the expression not the numerical value. I want to test and verify this integration whether it is supposed to be right. $\endgroup$ Commented Mar 14, 2015 at 0:48
  • $\begingroup$ I am sorry. I forgot to say the integration limits of this problem. All the upper limits are +infinity, and all the low limits are -infinity.I learnt this from an article that is Non‐Normal Stochastic Response of Linear Systems. This article wants the result as the expression not the numerical value. I want to test and verify this integration whether it is supposed to be right.@Nasser $\endgroup$ Commented Mar 14, 2015 at 0:55

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