A power of x past the twelfth beside a block is split off

BREAKING-CHANGES.md

@@ -205,6 +205,18 @@ partial fractions divide. It is taken out in front of the integral first
 | `"(b*d + 2*c*d*x)^9/(a + b*x + c*x^2)^3".ToEntity().Integrate("x")` | past a minute | 76,249 characters, the length the content-free one already had |
 | `"(b*d + 2*c*d*x)^8/(a + b*x + c*x^2)^3".ToEntity().Integrate("x")` | past a minute | 65,236 characters |
 
+### A power of x past the twelfth beside a block is split off
+
+**Answers where there were none.** `(c + d x^3 + g x^6 + f x^9)/(x^14 (a + b x^3))` was declined, and so were
+`x^13` to `x^17` beside `(a + b x^3)`, its square and its cube, Rubi's 1.1.3.8. The split that writes `N/(x^k B)` as
+`P/x^k + R/B`, with `P` the first `k` terms of the series of `N/B` at 0, took `k` up to 12. It takes `k` up to 24
+now, where the series costs one term per power
+([#718](https://github.com/asc-community/AngouriMath/issues/718)).
+
+| Input | Was (2.5.0) | Now |
+|---|---|---|
+| `"(c + d*x^3 + g*x^6 + f*x^9)/(x^14*(a + b*x^3))".ToEntity().Integrate("x")` | `integral(...)` | the antiderivative, in powers of x and the logarithms and arctangent of `a + b x^3`'s factors |
+
 ### A symbolic quadratic with a square discriminant is split into its linears before the division
 
 **Answers where there were none.** `(d + e x)^8/(a d e + (c d^2 + a e^2) x + c d e x^2)^2` ran past a minute, with

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

@@ -1245,7 +1245,7 @@ private static (Entity InY, Entity.Variable Y, Entity Shift)? InTheVariableThatD
                     pastTheSecondDegree |= TreeAnalyzer.TryGetPolynomial(written, x, out var terms) && terms.Keys.Any(power => power.CompareTo(EInteger.FromInt32(2)) > 0);
                 }
             }
-            if (k == 0 || k > MaximumPowerOfXBesideABlock || !pastTheSecondDegree || !block.ContainsNode(x) || !block.Vars.Any(symbol => symbol != x))
+            if (k == 0 || k > MaximumPowerOfXOverABlock || !pastTheSecondDegree || !block.ContainsNode(x) || !block.Vars.Any(symbol => symbol != x))
                 return null;
             if (!TreeAnalyzer.TryGetPolynomial(block, x, out var below) || !TreeAnalyzer.TryGetPolynomial(numerator, x, out var above))
                 return null;
@@ -1581,11 +1581,19 @@ Entity InU(Dictionary<EInteger, Entity> polynomial)
         }
 
         /// <summary>
-        /// The largest power of x, and the largest degree of the block beside it, that
-        /// <see cref="IntegrateOverAPowerOfXBesideABlock"/> takes: Rubi's suite goes to twelve.
+        /// The largest degree of a block beside a power of x that
+        /// <see cref="IntegrateOverAPowerOfXBesideABlock"/> takes; also the largest power of a
+        /// linear beside a block, and of x in blocks of <see cref="IntegrateOverBlocksInAPowerOfX"/>.
         /// </summary>
         private const int MaximumPowerOfXBesideABlock = 12;
 
+        /// <summary>
+        /// The largest power of x that <see cref="IntegrateOverAPowerOfXBesideABlock"/> takes. The
+        /// series it writes has one term per power of x, so the cost grows linearly in it. Rubi's
+        /// suite asks for up to <c>x^17</c>, beside <c>(a + b x^3)^3</c>.
+        /// </summary>
+        private const int MaximumPowerOfXOverABlock = 24;
+
         /// <summary>
         /// A polynomial over a power of a binomial, <c>P(x)/(a + b x^n)^k</c> with <c>n &gt;= 3</c>
         /// and <c>k &gt;= 2</c>, a power at a time down to <c>P'(x)/(a + b x^n)</c>, which

Sources/Tests/UnitTests/Calculus/AHighPowerOfXBesideABlockIntegralTest.cs

@@ -0,0 +1,45 @@
+//
+// 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>
+    /// A power of x past the twelfth beside a block with symbols in it is split off as the first
+    /// terms of the block's series at 0: Rubi's 1.1.3.8 asks for up to <c>x^17</c> beside
+    /// <c>(a + b x^3)^3</c>.
+    /// <a href="https://github.com/asc-community/AngouriMath/issues/718">#718</a>
+    /// </summary>
+    [Trait("Area", "Calculus")]
+    public sealed class AHighPowerOfXBesideABlockIntegralTest
+    {
+        [Theory]
+        [InlineData("(c + d*x^3 + g*x^6 + f*x^9)/(x^14*(a + b*x^3))")]
+        [InlineData("(c + d*x^3 + g*x^6 + f*x^9)/(x^17*(a + b*x^3))")]
+        [InlineData("(c + d*x^3 + g*x^6 + f*x^9)/(x^14*(a + b*x^3)^2)")]
+        public void DifferentiatesBack(string integrand)
+        {
+            var integral = integrand.ToEntity().Integrate("x");
+            Assert.DoesNotContain("integral(", integral.Stringize());
+            Entity Pinned(Entity e) => e.Substitute("a", 2).Substitute("b", 3).Substitute("c", 5)
+                .Substitute("d", -1).Substitute("g", 7).Substitute("f", 1);
+            var derivative = Pinned(integral.Substitute("C", 0)).Differentiate("x");
+            var original = Pinned(integrand.ToEntity());
+            foreach (var at in new[] { -1.7, -0.6, 0.45, 1.3 })
+            {
+                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)),
+                    $"d/dx of the antiderivative of {integrand} is {got} at x = {at}, where the integrand is {want}");
+            }
+        }
+    }
+}