How to find the parameters of an integral equation by fitting with given experimental data

I have experimental data X(independent variable), Y (Dependent variable)

X=[-2000 -1555.5 -1111.1 -666.6 -222.2 222.2 666.6 1111.1 1555.5 2000]

Y=[-5.70886E-5 -5.08756E-5 -4.45619E-5 -3.28869E-5 -1.20811E-5 2.03303E-5 3.67672E-5 4.48019E-5 5.06065E-5 5.60507E-5]

I want to find the parameters of integral equation mentioned below:

Y=0.4*A/C*Int[{(coth(t*X/446.6))-446.6/t*X}*exp(-ln(t/B)* ln(t/B))/2*C^2]dt

Limits of the integration are from 0 to inf(or some large value 50000)

Where A,B,C are parameters to determined so that above integral equation fits the above experimental data.

Approximate start values for A=1E17, B=200, C=1

As I am new to MATLAB, so please tell me how to write the code in MATLAB.