Ask the radicand rule's rewriting without the condition its inner simplification writes

BREAKING-CHANGES.md

@@ -542,6 +542,18 @@ becomes a polynomial in `u` times exponentials and trigonometric functions, and
 | `"(a+b*atan(c*x))^2/(1+i*c*x)^4".ToEntity().Integrate("x")` | `integral(...)` | 731 characters |
 | `"(a+b*atan(c*x))^3/(d+i*c*d*x)^4".ToEntity().Integrate("x")` | `integral(...)` | 1,202 characters |
 
+### Two roots of linears written as an inverse hyperbolic cosine's radicand are asked without a condition
+
+**Answers where there were none.** Rubi's 7.2.5 `x/(acosh(x) sqrt(x - 1) sqrt(x + 1))` ran past the budget. The pair of roots
+is written as the root of `x^2 - 1` that `acosh(x)` holds, with the factor `K` that is constant where it is defined.
+The inner simplification then wrote the rewritten question with `provided not x - 1 = 0` over the whole of it, and
+nothing below read that. The point it excludes is outside the integrand's domain, and the question is now asked
+without it ([#233](https://github.com/asc-community/AngouriMath/issues/233)).
+
+| Input | Was (2.5.0) | Now |
+|---|---|---|
+| `"x/(acosh(x)*sqrt(-1+x)*sqrt(1+x))".ToEntity().Integrate("x")` | `integral(...)` | 93 characters, `K Chi(acosh(x))` |
+
 ### An arcoth of a linear is integrated as its artanh plus a constant
 
 **Answers where there were none.** `acoth(x)^2/(1 - x^2)^2`, Rubi's 7.4.1, was declined, where

Sources/AngouriMath/Functions/Continuous/Integration/IndefiniteIntegralSolver.cs

@@ -43437,7 +43437,12 @@ Entity WithTheExponentials(Entity e, Entity? one)
                 (rewritten, root) = (paired, pairRoot);
             if (rewritten == expr)
                 return null;
-            var simplified = rewritten.InnerSimplified;
+            // Without a condition over the whole of it, which the inner simplification writes where a
+            // linear stands on both sides of the bar and nothing below reads: Rubi's 7.2.5
+            // `x/(acosh(x) sqrt(x - 1) sqrt(x + 1))` became `x/(K sqrt(x^2 - 1) acosh(x)) provided not
+            // x - 1 = 0`, and ran past the budget, where without the condition it is a `Chi`. The point
+            // it excludes is outside the integrand's domain.
+            var simplified = Functions.PartialFractions.Bare(rewritten.InnerSimplified);
             if (simplified == expr || simplified == expr.InnerSimplified)
                 return null;
             if (Integration.ComputeAsTheSameQuestion(simplified, x, integrateByParts) is not { } answer)

Sources/Tests/UnitTests/Calculus/TheRadicandRewritingAskedWithoutItsConditionIntegralTest.cs

@@ -0,0 +1,44 @@
+//
+// Copyright (c) 2019-2026 Angouri.
+// AngouriMath is licensed under MIT.
+// Details: https://github.com/asc-community/AngouriMath/blob/master/LICENSE.md.
+// Website: https://am.angouri.org.
+//
+
+using System;
+using AngouriMath.Extensions;
+using Xunit;
+
+namespace AngouriMath.Tests.Calculus
+{
+    /// <summary>
+    /// Two roots of linears written as the radicand an inverse hyperbolic cosine holds, asked without
+    /// the condition the inner simplification writes over the rewriting: Rubi's 7.2.5
+    /// <c>x/(acosh(x) sqrt(x - 1) sqrt(x + 1))</c> was asked as <c>... provided not x - 1 = 0</c> and ran
+    /// past the budget, where it is a hyperbolic cosine integral.
+    /// <a href="https://github.com/asc-community/AngouriMath/issues/233">#233</a>
+    /// </summary>
+    [Trait("Area", "Calculus")]
+    public sealed class TheRadicandRewritingAskedWithoutItsConditionIntegralTest
+    {
+        [Theory]
+        [InlineData("x/(acosh(x)*sqrt(-1 + x)*sqrt(1 + x))")]
+        [InlineData("x^2/(acosh(x)*sqrt(-1 + x)*sqrt(1 + x))")]
+        public void IsAnswered(string integrand)
+        {
+            var integral = integrand.ToEntity().Integrate("x");
+            var text = integral.Stringize();
+            Assert.DoesNotContain("integral(", text);
+            var derivative = integral.Substitute("C", 0).Differentiate("x");
+            var original = integrand.ToEntity();
+            foreach (var at in new[] { 1.2, 1.7, 2.3, 3.1, 4.4 })
+            {
+                var want = original.Substitute("x", at).EvalNumerical();
+                var got = derivative.Substitute("x", at).EvalNumerical();
+                Assert.True(Math.Abs((double)(got - want).RealPart) + Math.Abs((double)(got - want).ImaginaryPart)
+                            < 1e-9 * Math.Max(1, Math.Abs((double)want.RealPart) + Math.Abs((double)want.ImaginaryPart)),
+                    $"d/dx of the antiderivative of {integrand} is {got} at x = {at}, where the integrand is {want}");
+            }
+        }
+    }
+}