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

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

Maple 9

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

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

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

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

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

 >

```

```