Sounds reasonable to me. Go ahead
On Thu, 8 Jan 2026, 18:25 AB, <[email protected]> wrote:
> 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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