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Question: a integral embedded in Diff eq.....

Question:a integral embedded in Diff eq.....

magnetar 0 Maple 9
int
April 23 2012
0

i am solving for a system of df eq's, but the eq's have these little tricky integrals inside them.....so it either retards operation or no solutoin can be found...They look like...

 

B_12:=(10*a_2*a_3)*(u/( ((10^2+u)^(3/2)) * ((a_2^2+u)^(3/2)) * ((a_3^2+u)) )):

B_122:=(10*a_2*a_3)*(u/( ((10^2+u)^(3/2)) * ((a_2^2+u)^(5/2)) * ((a_3^2+u)) )):

B_123:=(10*a_2*a_3)*(u/( ((10^2+u)^(3/2)) * ((a_2^2+u)^(3/2)) * ((a_3^2+u)^(3/2)) )):

B_23:=(10*a_2*a_3)*(u/( ((10^2+u)) * ((a_2^2+u)^(3/2)) * ((a_3^2+u)^(3/2)) )):

B_33:=(10*a_2*a_3)*(u/( ((10^2+u)) * ((a_2^2+u)) * ((a_3^2+u)^(5/2)) )):

 
all of them are integrated from u=0..inf, 
 
$$ see attached paper and worksheet, regarding eq and worksheet.evolution_of_the_ell.pdf(Eq 17 and 19)
> 


B_12:=(10*a_2*a_3)*(u/( ((10^2+u)^(3/2)) * ((a_2^2+u)^(3/2)) * ((a_3^2+u)) )):
B_122:=(10*a_2*a_3)*(u/( ((10^2+u)^(3/2)) * ((a_2^2+u)^(5/2)) * ((a_3^2+u)) )):
B_123:=(10*a_2*a_3)*(u/( ((10^2+u)^(3/2)) * ((a_2^2+u)^(3/2)) * ((a_3^2+u)^(3/2)) )):
B_23:=(10*a_2*a_3)*(u/( ((10^2+u)) * ((a_2^2+u)^(3/2)) * ((a_3^2+u)^(3/2)) )):
B_33:=(10*a_2*a_3)*(u/( ((10^2+u)) * ((a_2^2+u)) * ((a_3^2+u)^(5/2)) )):
> 


solution:=array(1..25);
i:=1;
for a_2 from 1 to 5 do
        for a_3 from 1 to 5 do
        
        solution[i]:=evalf(int((10*a_2*a_3)*(u/( ((10^2+u)^(3/2)) * ((a_2^2+u)^(3/2)) * ((a_3^2+u)) )),u=0..infinity,method = _Gquad));

        i:=i+1;
        end do;
end do;
> 

 

solution := array(1 .. 25, [])

i := 1

> 

solution[1];
solution[2];
solution[3];
solution[15];
solution[25];

0.1001753068e-1

0.1277169978e-1

0.1337496638e-1

0.2004878825e-1

0.1975308642e-1

> 


solution:=array(1..25);
i:=1;
for a_2 from 1 to 5 do
        for a_3 from 1 to 5 do
        
        solution[i]:=evalf(int((10*a_2*a_3)*(u/( ((10^2+u)^(3/2)) * ((a_2^2+u)^(5/2)) * ((a_3^2+u)) )),u=0..infinity,method = _Gquad));
        i:=i+1;
        end do;
end do;
> 

 

solution := array(1 .. 25, [])

i := 1

> 

solution[1];
solution[2];
solution[3];
solution[15];
solution[25];

0.2549916900e-2

0.2421120520e-2

0.2084703207e-2

0.643476297e-3

0.3160493827e-3

> 


solution:=array(1..25);
i:=1;
for a_2 from 1 to 5 do
        for a_3 from 1 to 5 do
        
        solution[i]:=evalf(int((10*a_2*a_3)*(u/( ((10^2+u)^(3/2)) * ((a_2^2+u)^(3/2)) * ((a_3^2+u)^(3/2)) )),u=0..infinity,method = _Gquad));

        i:=i+1;
        end do;
end do;
> 

 

solution := array(1 .. 25, [])

i := 1

> 

solution[1];
solution[2];
solution[3];
solution[15];
solution[25];

0.4555557749e-2

limit(-(5/1411344)*(8700*(4+u)^(1/2)*(1+u)^(1/2)*11^(1/2)*(-1-u)^(1/2)*(-4-u)^(1/2)*EllipticF((1/24)*6^(1/2)*(100+u)^(1/2), (4/33)*6^(1/2)*11^(1/2))+87*(4+u)^(1/2)*(1+u)^(1/2)*11^(1/2)*(-1-u)^(1/2)*(-4-u)^(1/2)*EllipticF((1/24)*6^(1/2)*(100+u)^(1/2), (4/33)*6^(1/2)*11^(1/2))*u-205500*(4+u)^(1/2)*(1+u)^(1/2)*11^(1/2)*(-1-u)^(1/2)*(-4-u)^(1/2)*EllipticE((1/24)*6^(1/2)*(100+u)^(1/2), (4/33)*6^(1/2)*11^(1/2))-2055*(4+u)^(1/2)*(1+u)^(1/2)*11^(1/2)*(-1-u)^(1/2)*(-4-u)^(1/2)*EllipticE((1/24)*6^(1/2)*(100+u)^(1/2), (4/33)*6^(1/2)*11^(1/2))*u-105700*(4+u)^(1/2)*(1+u)^(1/2)*(100+u)^(1/2)-68369*(4+u)^(1/2)*(1+u)^(1/2)*(100+u)^(1/2)*u-685*(4+u)^(1/2)*(1+u)^(1/2)*(100+u)^(1/2)*u^2+2114000+2663640*u+554925*u^2+5285*u^3+34800*11^(1/2)*EllipticF((5/12)*6^(1/2), (4/33)*6^(1/2)*11^(1/2))+43848*11^(1/2)*EllipticF((5/12)*6^(1/2), (4/33)*6^(1/2)*11^(1/2))*u+9135*11^(1/2)*EllipticF((5/12)*6^(1/2), (4/33)*6^(1/2)*11^(1/2))*u^2+87*11^(1/2)*EllipticF((5/12)*6^(1/2), (4/33)*6^(1/2)*11^(1/2))*u^3-822000*11^(1/2)*EllipticE((5/12)*6^(1/2), (4/33)*6^(1/2)*11^(1/2))-1035720*11^(1/2)*EllipticE((5/12)*6^(1/2), (4/33)*6^(1/2)*11^(1/2))*u-215775*11^(1/2)*EllipticE((5/12)*6^(1/2), (4/33)*6^(1/2)*11^(1/2))*u^2-2055*11^(1/2)*EllipticE((5/12)*6^(1/2), (4/33)*6^(1/2)*11^(1/2))*u^3)/(400+504*u+105*u^2+u^3), u = infinity)

limit((5/216432216)*(-2029200*(9+u)^(1/2)*(1+u)^(1/2)*11^(1/2)*(-1-u)^(1/2)*(-9-u)^(1/2)*EllipticF((1/91)*91^(1/2)*(100+u)^(1/2), (1/33)*11^(1/2)*91^(1/2))-20292*(9+u)^(1/2)*(1+u)^(1/2)*11^(1/2)*(-1-u)^(1/2)*(-9-u)^(1/2)*EllipticF((1/91)*91^(1/2)*(100+u)^(1/2), (1/33)*11^(1/2)*91^(1/2))*u+15433500*(9+u)^(1/2)*(1+u)^(1/2)*11^(1/2)*(-1-u)^(1/2)*(-9-u)^(1/2)*EllipticE((1/91)*91^(1/2)*(100+u)^(1/2), (1/33)*11^(1/2)*91^(1/2))+154335*(9+u)^(1/2)*(1+u)^(1/2)*11^(1/2)*(-1-u)^(1/2)*(-9-u)^(1/2)*EllipticE((1/91)*91^(1/2)*(100+u)^(1/2), (1/33)*11^(1/2)*91^(1/2))*u+8165700*(9+u)^(1/2)*(1+u)^(1/2)*(100+u)^(1/2)+4937869*(9+u)^(1/2)*(1+u)^(1/2)*(100+u)^(1/2)*u+51445*(9+u)^(1/2)*(1+u)^(1/2)*(100+u)^(1/2)*u^2-244971000-274639710*u-29940900*u^2-272190*u^3-18262800*11^(1/2)*EllipticF((10/91)*91^(1/2), (1/33)*11^(1/2)*91^(1/2))-20474628*11^(1/2)*EllipticF((10/91)*91^(1/2), (1/33)*11^(1/2)*91^(1/2))*u-2232120*11^(1/2)*EllipticF((10/91)*91^(1/2), (1/33)*11^(1/2)*91^(1/2))*u^2-20292*11^(1/2)*EllipticF((10/91)*91^(1/2), (1/33)*11^(1/2)*91^(1/2))*u^3+138901500*11^(1/2)*EllipticE((10/91)*91^(1/2), (1/33)*11^(1/2)*91^(1/2))+155724015*11^(1/2)*EllipticE((10/91)*91^(1/2), (1/33)*11^(1/2)*91^(1/2))*u+16976850*11^(1/2)*EllipticE((10/91)*91^(1/2), (1/33)*11^(1/2)*91^(1/2))*u^2+154335*11^(1/2)*EllipticE((10/91)*91^(1/2), (1/33)*11^(1/2)*91^(1/2))*u^3)/(900+1009*u+110*u^2+u^3), u = infinity)

limit((1/2384928)*(-124000*(75+3*u)^(1/2)*(9+u)^(1/2)*91^(1/2)*(-9-u)^(1/2)*(-75-3*u)^(1/2)*EllipticF((1/15)*3^(1/2)*(100+u)^(1/2), (5/91)*3^(1/2)*91^(1/2))-1240*(75+3*u)^(1/2)*(9+u)^(1/2)*91^(1/2)*(-9-u)^(1/2)*(-75-3*u)^(1/2)*EllipticF((1/15)*3^(1/2)*(100+u)^(1/2), (5/91)*3^(1/2)*91^(1/2))*u+566500*(75+3*u)^(1/2)*(9+u)^(1/2)*91^(1/2)*(-9-u)^(1/2)*(-75-3*u)^(1/2)*EllipticE((1/15)*3^(1/2)*(100+u)^(1/2), (5/91)*3^(1/2)*91^(1/2))+5665*(75+3*u)^(1/2)*(9+u)^(1/2)*91^(1/2)*(-9-u)^(1/2)*(-75-3*u)^(1/2)*EllipticE((1/15)*3^(1/2)*(100+u)^(1/2), (5/91)*3^(1/2)*91^(1/2))*u+6372900*(75+3*u)^(1/2)*3^(1/2)*(9+u)^(1/2)*(100+u)^(1/2)+595285*(75+3*u)^(1/2)*3^(1/2)*(9+u)^(1/2)*(100+u)^(1/2)*u+5665*(75+3*u)^(1/2)*3^(1/2)*(9+u)^(1/2)*(100+u)^(1/2)*u^2-2867805000-462035250*u-17079372*u^2-127458*u^3-83700000*91^(1/2)*EllipticF((2/3)*3^(1/2), (5/91)*3^(1/2)*91^(1/2))-13485000*91^(1/2)*EllipticF((2/3)*3^(1/2), (5/91)*3^(1/2)*91^(1/2))*u-498480*91^(1/2)*EllipticF((2/3)*3^(1/2), (5/91)*3^(1/2)*91^(1/2))*u^2-3720*91^(1/2)*EllipticF((2/3)*3^(1/2), (5/91)*3^(1/2)*91^(1/2))*u^3+382387500*91^(1/2)*EllipticE((2/3)*3^(1/2), (5/91)*3^(1/2)*91^(1/2))+61606875*91^(1/2)*EllipticE((2/3)*3^(1/2), (5/91)*3^(1/2)*91^(1/2))*u+2277330*91^(1/2)*EllipticE((2/3)*3^(1/2), (5/91)*3^(1/2)*91^(1/2))*u^2+16995*91^(1/2)*EllipticE((2/3)*3^(1/2), (5/91)*3^(1/2)*91^(1/2))*u^3)/(22500+3625*u+134*u^2+u^3), u = infinity)

0.2386929030e-2

> 


solution:=array(1..25);
i:=1;
for a_2 from 1 to 5 do
        for a_3 from 1 to 5 do
        
        solution[i]:=evalf(int((10*a_2*a_3)*(u/( ((10^2+u)) * ((a_2^2+u)^(3/2)) * ((a_3^2+u)^(3/2)) )),u=0..infinity,method = _Gquad));

        i:=i+1;
        end do;
end do;
> 

 

solution := array(1 .. 25, [])

i := 1

> 

solution[1];
solution[2];
solution[3];
solution[13];
solution[25];

0.4677921942e-1

0.3952005843e-1

0.3165426703e-1

0.3705488869e-1

0.289603341e-1

> 


solution:=array(1..25);
i:=1;
for a_2 from 1 to 5 do
        for a_3 from 1 to 5 do
        
        solution[i]:=evalf(int((10*a_2*a_3)*(u/( ((10^2+u)) * ((a_2^2+u)) * ((a_3^2+u)^(5/2)) )),u=0..infinity,method = _Gquad));

        i:=i+1;
        end do;
end do;
> 

 

solution := array(1 .. 25, [])

i := 1

> 

solution[1];
solution[2];
solution[3];
solution[15];
solution[25];

0.2585966545e-1

0.9881035723e-2

0.4944121404e-2

0.337966834e-2

0.3664587570e-2

> 

 

 

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