P := d*e*f + b*c*f + a*b*d + a*c*e + d*c*e + d*c*f + e*b*d + e*b*f + a*f*d + a*f*e + b*c*d + b*c*e + a*b*e + a*b*f + a*c*d + a*c*f;
assume(a>0);                                                                
assume(b>0);
assume(c>0);  
assume(d>0); 
assume(e>0);
assume(f>0); 
int2 := int(1/P^2, a=0..infinity); 
int3 := factor(simplify(int(int2, b=0..infinity)));        
int4 := simplify(int(int3, c=0..infinity)); 
int5 := simplify(int(int4, d=0..infinity));    

evalf(int(simplify(subs(e=1, int5)), f=0..infinity));  
evalf(6*Zeta(3));