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Original Message (ID '128479') By Bill Simpson:
Simplify does not understand it can factor an expression independent of the variable of integration outside the integral. A user replacement rule can make this happen. In[1]:= Simplify[Integrate[f[x,z]Sin[θ],{z,0,1}] /.Integrate[q_*r_,{v_,l_,h_}] /;FreeQ[r,v] :> r*Integrate[q,{v,l,h}]-Sin[θ]Integrate[f[x,z],{z,0,1}]] Out[1]= 0 Test this very carefully. Think about zeros and infinities and all the other special cases that can happen. User replacement rules are difficult to get right and can easily result in errors. It is also possible that //. or ReplaceRepeated might be needed in place of /. or Replace if you happen to have more than one factor in the integrand that is independent of the variable of integration.