Numerical Integration from -Inf to Inf

Problem: I have the following integral which i need to evaluate numerically.

Now i have to do this for different values of c and γ, but for now let us say c=0.1 and

My attempt: After reading few already available answers and documentation, i tried the following

gamma =3;
fun = @(x) (x.*exp(-x.^2)).*(((x+0.1).^2) .* (exp(2.*(x+0.1).^2 .*gamma.^2)));
format long
q1 = integral(fun,-Inf,Inf,'RelTol',1e-8,'AbsTol',1e-13)

Result: The output i get is Nan

Any help or advice will be helpful to me.

Thanks.

Answer 1

[Birdman]

Try the symbolic approach and consider the problem as follows:

syms x
F(x)=x*(x+0.1)^2*exp(2*(x+0.1)^2*3^2)*exp(-x^2);

After this point, you need to break it down to two pieces while calculating integral:

INT1=int(F,x,-inf,0);
INT2=int(F,x,0,inf);

The sum of these two will give the correct result.

[Vira Roy]

Thanks for the answer Birdman, but the result is still the same. INT1 outputs -Inf while INT2 outputs Inf. Am i missing something obvious here.

Thank you.

[Birdman]

I think you don't miss anything. Just plot the function for some x values and see if -Inf and Inf outputs make sense or not:

x=-5:0.001:5;
plot(x,F(x))

[Vira Roy]

Birdman,

The graph is coming out to be fine, but what i was looking for was some specific value for the integral so that i can later plot that obtained result for varying values of gamma(which i have taken to be 3 here but plan to obtain a continous graph for all possible values of gamma)

Is there someway to do that from what you sugggested above.

Thank you, and sorry for being bit blunt here. You help is dearly appreciated.