Integration with one variable and many constants

Hello,

I have a problem where I would like to inegrate this function:

f(x) = exp(-g*(a-x)^2)./(((x-b).^2+c^2).*((x-d).^2+e^2));

where a,b,c,d,e,g are constants, and the variable is x.

My attempt was:

syms a b c d e g x real

f = exp(-g*(a-x)^2)/(((x-b)^2+c^2)*((x-d)^2+e^2)); Q = int(f,0,inf)

But it just returns:

Q =

int(exp(-g*(a - x)^2)/((c^2 + (b - x)^2)*(e^2 + (d - x)^2)), x, 0, Inf).

I don't know what I'm doing wrong, and whether or not my solution even converges or not, because I tried this with Mathematica and it doesn't give me an output either. I've even tried to modify the function to:

f = (a-x)*exp(-g*(a-x)^2)/(((x-b)^2+c^2)*((x-d)^2+e^2));

But even that doesn't work. Any help would be greatly appreciated.

[Abdurrahman M]

I have even tried this:

syms a b c d e g x real

f = @(x) (a-x)*exp(-g*(a-x)^2)/(((x-b)^2+c^2)*((x-d)^2+e^2)); Q = integral(f,0,inf)

But I get a lot of errors

[Abdurrahman M]

I've simplified the function by putting in the constants:

f(x,y)=g(x)*exp(-1.02*(1-y)^2)/(((y-x)^2+1.05)*((y-x+3351)^2+0.0841))

In my case, g(x) is a two column vector.

Where I have to integrate with respect to x and y from 0 infinity.

Answer 1

[Mischa Kim]

Abdurrahman, there is no closed-form solution that MATLAB (and Mathematica) can compute. That is why you get int() term as a result.

So in other words, you would have to integrate numerically and for that you need numeric values for your constants.

[Abdurrahman M]

The problem is that after I integrate with respect to x, I have to then integrate the resulting function with respect to y, of which the constants c(y) and d(y) are functions of, which I have not written explicitely.