MATLAB: How to remove some specific terms from a function

remove terms

Dear sir, I am trying to write a code that can generate the specific terms from certain function. However, I just cannot find a way to remove the exponential terms. I have a list of functions that generate by same function, that all look like f=a!*sqrt(b+c*i)*exp(-dk+sqrt(b+c*i)), where a,b,c,d are all changing variable. I want to remove all the terms of exp(), so as to use the first two part for next step of calculation. How to do this? Thank you.
To be concrete, here is my formula sheet.
if true
format long;
h=1.05457173e-34;
t=1e25*365*24*3600;
m=60;
a=1/1000;
syms x k;
int(exp(i*k*x-i*h*k^2*t/(2*m)-k^2*a^2/2),k,-Inf,Inf)
f=pi^(1/2)*(sqrt(a/(2*pi^(3/2))))/((10126067097211690078125*i)/365375409332725729550921208179070754913983135744+ 1/2000000)^(1/2)
g=pi^(1/2)*(sqrt(a/(2*pi^(3/2))))/((158219798393932657470703125*i)/5708990770823839524233143877797980545530986496+1/2000000)^(1/2)
u=pi^(1/2)*(sqrt(a/(2*pi^(3/2))))/(27714145064399998094084151567728884845503502656025676347457107551846400*i+ 1/2000000)^(1/2)
o=pi^(1/2)*(sqrt(a/(2*pi^(3/2))))/((1756592631284943967788998796645*i)/633825300114114700748351602688+ 1/2000000)^(1/2)
q=pi^(1/2)*(sqrt(a/(2*pi^(3/2))))/((89937542721789151668027362145*i)/324518553658426726783156020576256+ 1/2000000)^(1/2)
Z=(real(f))^2;
SD=1/(sqrt(2*pi)*Z)
end
The f g u o q, is some example with different t I done, but actually I need to do for more than 100 times for data analysis. As you see, the integral will generate sth with exp(),and f g u o q are all eliminated by myself.

Best Answer

For that h and m, and holding a and t symbolic, but assuming a is real and assuming t is positive:
    YourIntegral = 284475670516978489457516559826613190 * exp(-284475670516978489457516559826613190 * x^2 / (i*t + 568951341033956978915033119653226380 * a^2)) * 2^(1/2) * pi^(1/2)/ ((142237835258489244728758279913306595*i) * t + 80926407116084504595296678347317302904777180422918746308915785881976100 * a^2)^(1/2)
To get to this form instead of a piecewise form, before you do the integral use assume() to add the assumptions about a and t
assume(t > 0 & a > 0)
and you might need to simplify() the result of the integral.
By examination we can see that the x variable exists as a multiplier of the numerator of the exp() term, and does not otherwise appear anywhere in the integral. So to get rid of the exp() term,
exp_removed = subs(YourIntegral, x, sym(0));
Now if you want you could turn it into a numeric procedure with a and t as parameters:
f = matlabFunction( simplify(exp_removed), 'vars', {a, t});
Note: the result is going to be complex.
Also note: there is no factorial or gamma function involved.
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