Start by making a preliminary PR in the module(either for existing issues 
<https://github.com/sympy/sympy/issues?q=is%3Aopen+is%3Aissue+label%3Aintegrals.manualintegrate>
 
or improving the functionality). Then by looking at your changes we can 
suggest improvements and guide you further.

On Saturday, March 9, 2019 at 7:07:14 AM UTC+5:30, Nabanita Dash wrote:
>
> Greetings.
> I am participating in GSoC 2019 under SymPy and I want to do the following 
> tasks for the development of search-based solution and step-by-step as well 
> as enhance transolve module.
> Tasks to be done under search-based solution and step-by step
>
>    - Apply various set transformations on the given set.
>
>
>    - Define a metric of the usability of solutions, or a notion of some 
>    solutions being better than others.
>
>
>    - Different transformations would be the nodes of a tree.
>
>
>    - Suitable searching techniques could be applied to get the best 
>    solution.
>
>  As,said by Aaron Meurer (@asmeurer) I have started checking how manual 
> integrate works.Please help me guide through this.SymPy is an interesting 
> project,so I will continue to contribute even if I don't get selected in 
> GSoC19.
>

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