Hi everyone,
I would like to work on a TODO found in sympy/integrals/manualintegrate.py
inside the sqrt_quadratic_rule function:
elif n == -1:
generic_step = sqrt_quadratic_denom_rule(f_poly, integrand)
else:
return # todo: handle n < -1 case
return _add_degenerate_step(generic_cond, generic_step, degenerate_step)
This TODO handles integrals involving odd negative powers of a quadratic,
such as (a + bx + cx**2) ** {-3/2}, (a + bx + cx**2) ** {-5/2}, etc.
Proposed Plan:
I plan to implement a recursive reduction step using the formula from
Gradshteyn & Ryzhik (2.263.3).
[image: Screenshot 2026-01-08 230124.png]
This formula rewrites integrals of the form integral(dx / sqrt(R **
(2k+1))) in terms of an algebraic term and a simpler integral integral(dx /
sqrt(R ** (2k-1))). By applying this recursively, any n < -1 case can be
reduced until it reaches the n = -1 base case, which is already correctly
handled by the existing sqrt_quadratic_rule.
*Questions:*
1.
Is anyone currently working on this?
2.
Are there any known blockers for this implementation?
If there are no objections, I would like to proceed with the implementation
and a PR.
Thanks,
Ayush Bothra
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