I have been writing a Homotopy approximation method solver for differential equations. This requires the use of integration, So far I have been using a very simple function for the integration of polynomials. This is clearly the weakest link in what I am doing so far. The problem of course is that what I want to do will require that I integrate more complicated functions then just polynomials.

For those that are interested here is the code that I am using for my Homotopy approximations.

What I would like to know is how far off in the future will it be before a usable symbolic integrator capable of this kind of thing will exist, or does one already exist? In other words is there something that is already out that I just have not yet found, is this something that is already in the works and just a matter of time, or am I better off trying to write something that is capable of doing what I need.

I have already found SymbolicNumericIntegration.jl and unfortunately I quickly found that it is not yet capable of handling the equations that I am integrating, since as soon as I attempted to integrate functions including multiple symbolic variables it just starts giving incorrect answers. This appears to be a know issue.

For what I am trying to do I will need the ability to integrate things like Fourier series, exponential functions and Pade representations, of course other things are going to come up but I am sure that this gives a good idea of what I am trying to find.