Read a power of a power of a linear beside an exponential of a linear

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

@@ -543,10 +543,15 @@ private static bool TakeMomentFactor(Entity factor, bool inverted, Entity.Variab
                     return sum;
                 }
 
-            // A power of a linear with an offset, beside an exponential of a linear.
+            // A power of a linear with an offset, beside an exponential of a linear -- or a power of a power of one,
+            // ((c + d x)^n)^m, which stands as written where (c + d x)^(n m) would: its logarithmic derivative is
+            // n m d/(c + d x) on every branch, and that is all the answer asks of it.
             if (factorsInX != 1 || !degree.Equals(Entity.Number.Integer.One)
-                || single is not Entity.Powf(var linear, var exponentOfLinear) || exponentOfLinear.ContainsNode(x)
-                || !TreeAnalyzer.TryGetPolyLinear(linear, x, out var slope, out var offset)
+                || single is not Entity.Powf(var linear, var exponentOfLinear) || exponentOfLinear.ContainsNode(x))
+                return null;
+            while (linear is Entity.Powf(var innerLinear, var innerExponent) && !innerExponent.ContainsNode(x))
+                (linear, exponentOfLinear) = (innerLinear, (innerExponent * exponentOfLinear).InnerSimplified);
+            if (!TreeAnalyzer.TryGetPolyLinear(linear, x, out var slope, out var offset)
                 || !TreeAnalyzer.TryGetPolyLinear(term, x, out var rate, out _))
                 return null;
             var exponentOfPower = singleBelow ? (-exponentOfLinear).InnerSimplified : exponentOfLinear;

Sources/Tests/UnitTests/Calculus/APowerBesideAnExponentialOfAPowerIntegralTest.cs

@@ -205,6 +205,16 @@ public void APositiveRateIsTakenOutOfThePower()
         [InlineData("x^2*e^(b*(1 + 4*x + 6*x^2 + 4*x^3 + x^4))")]
         public void AnExponentThatIsAPowerOfAShiftedLinearWrittenExpanded(string integrand) => DifferentiatesBack(integrand);
 
+        /// <summary>
+        /// A power of a power of a linear, <c>((d + f x)^n)^m</c>, which is not <c>(d + f x)^(n m)</c> off the right half-line
+        /// but has its logarithmic derivative, and stands as written in the answer where that power would. Rubi's 2.1.
+        /// </summary>
+        [Theory]
+        [InlineData("c^(a + b*x)*((d + f*x)^n)^m")]
+        [InlineData("e^(b*x)/((d + f*x)^n)^m")]
+        [InlineData("e^(-x)*((x + d)^2)^m")]
+        public void APowerOfAPowerOfALinear(string integrand) => DifferentiatesBack(integrand);
+
         /// <summary>
         /// A power that is not whole of an inverse sine or cosine, which the substitution that undoes it writes as a power of
         /// u beside a polynomial in the sine and cosine of u, Euler's formula's exponentials of <c>i u</c>, each a gamma