Function foldLnExponentialE

src/compute-engine/rubi/rubi-utils.ts:3910–3933

(
  ce: ComputeEngine,
  e: Expression
)

        return cosE;
      case 'Tan':
        return sinE.div(cosE);
      case 'Cot':
        return cosE.div(sinE);
      case 'Sec':
        return ce.One.div(cosE);
      case 'Csc':
        return ce.One.div(sinE);
    }
  }
  return ce.function(
    u.operator,
    u.ops.map((o) => substForTrig(o, sinE, cosE, v, ce))
  );
}

/** SubstFor[v, u, x] — u with the trig subexpression `v` replaced by `x`
 * (u is a function of v). Returns null when v isn't a handled trig target. */
function substFor3(v: Expression, u: Expression, ctx: Ctx): Expression | null {
  const ce = ctx.ce;
  const X = ce.symbol(ctx.x);
  const vt = substTrigNode(v, ctx.x, ce);
  if (vt === null) return null;
  // d ≠ 1 (a free factor on the substitution variable) is not handled here.
  if (!selectFactors(v, ctx.x, ce, true).isSame(1)) return null;
  const arg = vt.ops![0];
  const sqrt1m = ce.function('Sqrt', [ce.One.sub(X.pow(2))]); // √(1−x²)
  const sqrt1p = ce.function('Sqrt', [ce.One.add(X.pow(2))]); // √(1+x²)