Hello community,

I am considering applying to GSoC 2026 to work under the sympy org. An idea 
which I've taken an interest in and explored a bit is extending 
manualintegrate 
<https://github.com/sympy/sympy/wiki/GSoC-Ideas#rule-based-symbolic-integration>.
 
I have gone through the code and the run the test cases to see where 
manualintegrate is used and I believe I have a decent idea of the flow of 
control which leads to calls to manualintegrate. 

In particular, I noticed that solving issues like Issue 16396 
<https://github.com/sympy/sympy/issues/16396> which are addressed in 
test_failing_integrals.py, which should be easy for a student to calculate 
using change of variables and integration identities could be a target for 
the project. An ambitious target could also be to be able to compute the 
antiderivative analytically like it is done over here 
<https://www.integral-calculator.com/#expr=1/(1+sqrt(tanx)>. I believe they 
use a combination of manual identities and a complete implementation of 
Risch algorithm, which is also something I would be interesting in going 
for in case there are ideas around it. 

I have my dev environment set up and I have submitted 2 bug-fixing PRs to 
sympy in the past. I don't have a college math background to be able to 
understand stuff like Risch algorithm well, but I am open to learning. Due 
to time constraints, I would prefer to take on a 90-hour project. 

I would appreciate guidance from the community on how best to proceed from 
here.

Thanks and regards,
ButteryPaws (on github).

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