Ayush Bothra enhanced symbolic integration routines in the sympy/sympy repository, focusing on differential equations and quadratic forms. He implemented a hypertangent test for Risch differential equations to validate integration logic and introduced recursive reduction for integrals involving higher odd powers of quadratic forms, referencing established mathematical tables. Addressing edge cases, Ayush fixed branch-cut handling in the sqrt_quadratic_reduction_rule and expanded automated test coverage to ensure reliability for complex integral scenarios. His work, using Python and leveraging skills in mathematics and symbolic computation, improved the robustness and accuracy of integral evaluation, reducing manual intervention and supporting more comprehensive symbolic modeling.