Problem with integration need help

Hi guys,

The next code is to solve an integration. The code will keep running without show any result. Please, need your help if you know the reason.

The code is;

syms T1 T2 r1 r2 r w m k Tb
clc
b=(-4*m*w^2*r1^4)/(k*(r2^2-r1^2));
c1=((T2-T1)+(b*r2^2/4)*(((r2/r1)^2)-1))/(log(r2/r1));
c2=T1-((b*r2^4)/(4*r1^2))-(((T2-T1)+(b*r2^2/4)*(((r2/r1)^2)-1))/(log(r2/r1)))*log(r1);
Tb=(int((((c1*r/2)+(c2/r))*((b*r2^4/4*r^2)+(c1*log(r)+c2))*r),r,r1,r2))/....
   (int(((((-2*w*r1^2)/(r2^2-r1^2))*(r/2))+(((w*r1^2*r2^2)/(r2^2-r1^2))*(1/r)))*r,r,r1,r2));

Answer 1

[Walter Roberson]

Try breaking Tb up into two pieces, numerator and denominator, so that you can figure out which of the two integrations is giving the problem.

In my tests with a different mathematics system, the integrations were fast.

[Abdulaziz]

Hi Walter your suggestion was really helpful the problem was in the numerator but i still can not find why

[Walter Roberson]

In both your original equation and the modified one you give about half an hour ago, none of the b, c1, or c2 involve "r". Because of that, you can do the integration just by

syms b c1 c2 r1 r2 r
Tb1 = int((((c1*r/2)+(c2/r))*((b*r2^4/4*r^2)+(c1*log(r)+c2))*r),r,r1,r2);

and then take that result and substitute in the values for b, c1, c2:

b=(-4*m*w^2*r1^4)/(k*(r2^2-r1^2));
c1=((T2-T1)+(b*r2^2/4)*(((r2/r1)^2)-1))/(log(r2/r1));
c2=T1-((b*r2^4)/(4*r1^2))-(((T2-T1)+(b*r2^2/4)*(((r2/r1)^2)-1))/(log(r2/r1)))*log(r1);

Tb = subs(Tb1);

As the integral will be simpler, it is less likely that it will run indefinitely.

Answer 2

[Abdulaziz]

the code is simplify like next:

clear all 
syms T1 T2 r1 r2 r w m k Tb
clc
b=(-4*m*w^2*r1^4)/(k*(r2^2-r1^2));
c1=((T2-T1)+(b*r2^2/4)*(((r2/r1)^2)-1))/(log(r2/r1));
c2=T1-((b*r2^4)/(4*r1^2))-(((T2-T1)+(b*r2^2/4)*(((r2/r1)^2)-1))/(log(r2/r1)))*log(r1);
Tb=(int((((c1*r/2)+(c2/r))*((b*r2^4/4*r^2)+(c1*log(r)+c2))*r),r,r1,r2));

the processor is running endlessly to solve the integration until i stop it by ctl/c