Integration with one variable and many constants

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Abdurrahman M
Abdurrahman M 2016-10-20
评论： Abdurrahman M 2016-10-20
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.
  2 个评论
Abdurrahman M
Abdurrahman M 2016-10-20
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
Abdurrahman M 2016-10-20
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.

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采纳的回答

Mischa Kim
Mischa Kim 2016-10-20
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.
  1 个评论
Abdurrahman M
Abdurrahman M 2016-10-20
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.

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