# How to do this triple integral?

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?

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_]

• Your figure is illegible. Please post copyable code. – David G. Stork Mar 13 '15 at 1:39
• you should not have the underscores in the last expression – george2079 Mar 13 '15 at 3:14

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]


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


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

• 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. – whdwpy666 Mar 14 '15 at 0:48
• 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 – whdwpy666 Mar 14 '15 at 0:55