Sky-Bj

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These are replies submitted by Sky-Bj

@mmcdara Sorry. I edited it

Thank you for your guidance

Can this integral(I wrote above) be solved without bounds?
Actually, I need to get the parameter (N ) in terms of phi.

restart

V := m^4*(varphi/M)^p;

m^4*(varphi/M)^p

(1)

V1 := diff(V, varphi);

m^4*(varphi/M)^p*p/varphi

(2)

V2 := diff(V1, varphi)

m^4*(varphi/M)^p*p^2/varphi^2-m^4*(varphi/M)^p*p/varphi^2

(3)

f := Zeta * (varphi^2)

Zeta*varphi^2

(4)

f1 := diff(f, varphi)

2*Zeta*varphi

(5)

f2 := diff(f1, varphi)

2*Zeta

(6)

R:= simplify((V/3-f1*V1/3*V)/((1-kappa^2*f)/12*kappa^2+f1/V))

-4*m^8*(-2*(varphi/M)^(3*p)*Zeta*m^4*p+(varphi/M)^(2*p))/((varphi/M)^p*Zeta*kappa^4*m^4*varphi^2-kappa^2*m^4*(varphi/M)^p-24*Zeta*varphi)

(7)

N := int(3*V1*kappa^2*((2*V*V1)/3 - f1^2*V1*R/(3*V) - f1*V1^2/(3*V))/(V*(-f*kappa^2 + 1)*(-R*f1 - 2*V1)), varphi=varphi__c..varphi__f);

int(3*p*kappa^2*((2/3)*m^8*((varphi/M)^p)^2*p/varphi+(16/3)*Zeta^2*varphi*m^8*p*(-2*(varphi/M)^(3*p)*Zeta*m^4*p+(varphi/M)^(2*p))/((varphi/M)^p*Zeta*kappa^4*m^4*varphi^2-kappa^2*m^4*(varphi/M)^p-24*Zeta*varphi)-(2/3)*Zeta*m^4*(varphi/M)^p*p^2/varphi)/(varphi*(-Zeta*kappa^2*varphi^2+1)*(8*m^8*(-2*(varphi/M)^(3*p)*Zeta*m^4*p+(varphi/M)^(2*p))*Zeta*varphi/((varphi/M)^p*Zeta*kappa^4*m^4*varphi^2-kappa^2*m^4*(varphi/M)^p-24*Zeta*varphi)-2*m^4*(varphi/M)^p*p/varphi)), varphi = varphi__c .. varphi__f)

(8)

Digits:=4

4

(9)

NN:=evalf(subs([p=2, Zeta=1/6,M = 1, m = 1, kappa=1], N));

int(6.*(1.333*varphi^3+.2963*varphi*(-.6667*varphi^6+varphi^4)/(.1667*varphi^4-1.*varphi^2-4.*varphi)-.4444*varphi)/(varphi*(-.1667*varphi^2+1.)*(1.333*varphi*(-.6667*varphi^6+varphi^4)/(.1667*varphi^4-1.*varphi^2-4.*varphi)-4.*varphi)), varphi = varphi__c .. varphi__f)

(10)

 

 

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