Symbolic integration when the answer is not in a closed form

I want to integrate the expression tanh(T(x^2 + G^2)^(1/2))/(x^2 + G^2)^(1/2) from 0 to a. Here I can input a row matrix for T values, so that G should be obtained as a function of T and a. The integral does not exist in a closed form, and hence must be done numerically while still retaining parameters. From what I read, integration using the symbolic toolbox cannot handle integrals that do not have closed form solutions. Please help.

[Walter Roberson]

Integrate with respect to x?

Is that T multiplied by the expression, or T indexed at the expression?

How can you obtain G a a function of T and a if you do not know what the integral evaluates to? Your expression has five implicit parameters: 1) what the integral is equal to; 2) T; 3) G; 4) x; 5) a. You know T and a and x falls out during the integration -- but that leaves what the integral is equal to and leaves G, two parameters.

[Varada]

Hi Walter, Sorry for not being clear. It is T multiplied by the expression in the brackets, and the integral is with respect to x. I know what the integral evaluates to, it is a function of the parameter a, which is a constant.

[Walter Roberson]

Okay so what does the integral evaluate to?

Answer 1

[arvind thakur]

only closed form integral can solve by int function

[Walter Roberson]

int() can create closed form solutions for some (but not all) functions that have closed form integral solutions.

int() cannot create closed form solutions for any function that does not have a closed form integral solution.

So if int() returns something that is not closed form, there are three possibilities:

1. No closed form integral exists for the expression; OR
2. No closed form integral for the expression is known to current mathematics (so MATLAB could not be expected to solve it); OR
3. Techiques to solve the integral in closed form exist, but MATLAB does not implement them yet; some might be rare and difficult to compute, some might just not be implemented yet due to limited funding and limited time