What is the concern with the result that was returned? It looks like the SMT came back with the best answer it could with the information it was given. The form of the result would be a bit simpler by putting assumptions on 'a' if sensible to do so:
>> syms a positive
>> int(x*exp(-a*x)/(x^2+1),x,[0 inf])
ans =
(2*meijerG(1, [], [1, 1, 3/2], [], a^2/4))/(a^2*pi^(1/2))
But until a value is assigned to 'a' what shold the expected result be? Of course, the integral can be evaluated at a value of interest:
>> f(a)=int(x*exp(-a*x)/(x^2+1),x,[0 inf])
f(a) =
(2*meijerG(1, [], [1, 1, 3/2], [], a^2/4))/(a^2*pi^(1/2))
>> vpa(f(5))
ans =
0.033896
Best Answer