Symbolic integration when the answer is not in a closed form

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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.
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Answers (1)

arvind thakur
arvind thakur on 25 Sep 2021
only closed form integral can solve by int function
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Walter Roberson
Walter Roberson on 25 Sep 2021
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

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