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Question: Adding assumptions to variables to simplify integral

Question:Adding assumptions to variables to simplify integral

astroLaura 10 Maple 2016
integration assumptions simplification
August 20 2019
2

Hello,

I'm new to Maple, but somewhat competent in computer mathematics. Below is some code that I wrote. I start off with f, my original function, and try to simplify it. I tried defining some assumptions as best I could. When I calculate the integral, it gives me an odd range of validity.

I'm wondering if I can further add to my assumptions to make the integral result more concise, i.e. without the piecewise range of validity. All my variables in f and g are already real and positive, so there is no reason one of the expressions should be less than zero. 

Thank you in advance for any insight.

 flat-geometry_recalc_Aug20_singleS.mw
 

f := (Pi*x+2*c+2*m)/(mu__c*S)+2*epsilon/(mu__a*S)+(Pi*x+2*c)/(mu__s*S)

(Pi*x+2*c+2*m)/(mu__c*S)+2*epsilon/(mu__a*S)+(Pi*x+2*c)/(mu__s*S)

 (1)

g := simplify(f, symbolic)

(((Pi*x+2*c+2*m)*mu__s+2*((1/2)*Pi*x+c)*mu__c)*mu__a+2*epsilon*mu__c*mu__s)/(mu__c*S*mu__a*mu__s)

 (2)

`assuming`([g], [S__s::positive]); 1; S__c::positive, S__a::positive, epsilon::positive, mu__s::positive, mu__c::positive, mu__a::positive, c::positive, m::positive

S__c::positive, S__a::positive, epsilon::positive, mu__s::positive, mu__c::positive, mu__a::positive, c::positive, m::positive

 (3)

int(1/g, x = 0 .. w, AllSolutions)

`assuming`([int(1/g, x = 0 .. w)], [0 < w])

piecewise(And((c*mu__a*mu__c+c*mu__a*mu__s+epsilon*mu__c*mu__s+m*mu__a*mu__s)/(mu__a*(mu__c+mu__s)) < 0, -2*(c*mu__a*mu__c+c*mu__a*mu__s+epsilon*mu__c*mu__s+m*mu__a*mu__s)/(Pi*mu__a*(mu__c+mu__s)) < w), undefined, mu__s*S*mu__c*(-ln(2)-ln(c*mu__a*mu__c+c*mu__a*mu__s+epsilon*mu__c*mu__s+m*mu__a*mu__s)+ln(Pi*mu__a*mu__c*w+Pi*mu__a*mu__s*w+2*c*mu__a*mu__c+2*c*mu__a*mu__s+2*epsilon*mu__c*mu__s+2*m*mu__a*mu__s))/(Pi*(mu__c+mu__s)))``

 (4)

 

NULL


 

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