diff --git a/Sources/AngouriMath/Functions/Continuous/Integration/IndefiniteIntegralSolver.cs b/Sources/AngouriMath/Functions/Continuous/Integration/IndefiniteIntegralSolver.cs
index a5cfa4a96..b0414ac96 100644
--- a/Sources/AngouriMath/Functions/Continuous/Integration/IndefiniteIntegralSolver.cs
+++ b/Sources/AngouriMath/Functions/Continuous/Integration/IndefiniteIntegralSolver.cs
@@ -18385,7 +18385,8 @@ private static (Entity Logarithm, Entity Degree, Entity Offset, Entity Slope)? T
 
         /// <summary>
         /// Whether <paramref name="factor"/> is a power that is not whole of something holding a logarithm of something in
-        /// <paramref name="x"/>, or an exponential of something in <paramref name="x"/> that is not linear in it.
+        /// <paramref name="x"/>, an exponential of something in <paramref name="x"/> that is not linear in it, or holds a
+        /// sine or a cosine of one.
         /// </summary>
         private static bool IsATranscendentalPowerOfSomethingInX(Entity factor, Entity.Variable x) => factor switch
         {
@@ -18394,8 +18395,13 @@ private static (Entity Logarithm, Entity Degree, Entity Offset, Entity Slope)? T
                 => exponent.Nodes.Any(node => node is Sumf or Minusf && node.ContainsNode(x))
                     && !TreeAnalyzer.TryGetPolyLinear(exponent, x, out _, out _),
             Powf(var @base, var exponent) when !exponent.ContainsNode(x) && exponent is not Number.Integer
-                => @base.Nodes.Any(node => node is Logf(_, var antilogarithm) && antilogarithm.ContainsNode(x)),
-            _ => false
+                && @base.Nodes.Any(node => node is Logf(_, var antilogarithm) && antilogarithm.ContainsNode(x)) => true,
+            // A sine or a cosine of a sum in x that is not linear, in whatever holds it: x sin(a + b (c + d x)^3), and
+            // x (a + b sin(c + d (f + g x)^n))^2, which in u are powers of u beside the sine of a power of u, Euler's
+            // formula's exponentials. Rubi's 4.1.12.
+            _ => factor.Nodes.Any(node => node is Sinf or Cosf && node.DirectChildren.First() is var argument && argument.ContainsNode(x)
+                && argument.Nodes.Any(inner => inner is Sumf or Minusf && inner.ContainsNode(x))
+                && !TreeAnalyzer.TryGetPolyLinear(argument, x, out _, out _))
         };
 
         /// <summary>
diff --git a/Sources/Tests/UnitTests/Calculus/APowerBesideAnExponentialOfAPowerIntegralTest.cs b/Sources/Tests/UnitTests/Calculus/APowerBesideAnExponentialOfAPowerIntegralTest.cs
index 4d2473448..4b9f2c7a2 100644
--- a/Sources/Tests/UnitTests/Calculus/APowerBesideAnExponentialOfAPowerIntegralTest.cs
+++ b/Sources/Tests/UnitTests/Calculus/APowerBesideAnExponentialOfAPowerIntegralTest.cs
@@ -126,14 +126,19 @@ public void APositiveRateIsTakenOutOfThePower()
 
         /// <summary>
         /// A polynomial beside a symbolic power of a logarithm of one shifted linear, or an exponential of a power of one,
-        /// written in <c>u = a + b x</c>, where each term is a gamma function. The constant in front comes along. Rubi's 3.3,
-        /// 3.4 and 2.3.
+        /// written in <c>u = a + b x</c>, where each term is a gamma function. The constant in front comes along. And beside
+        /// a sine or a cosine of a power of one, which in u is Euler's formula's exponentials of a power of u. Rubi's 3.3,
+        /// 3.4, 2.3 and 4.1.12.
         /// </summary>
         [Theory]
         [InlineData("2*x*(a + b*ln(c*(d + f*x)))^n")]
         [InlineData("x*(a + b*ln(c*(d + f*sqrt(x))))^n")]
         [InlineData("x^2*f^(c*(a + b*x)^3)")]
         [InlineData("(a + b*x)^2*e^(-c*(d + f*x)^3)")]
+        [InlineData("(a + f*x)*sin(b + c*(d + f*x)^3)")]
+        [InlineData("x*sin(a + b*(c + d*x)^n)")]
+        [InlineData("x^2*cos(a + b/(c + d*x)^3)")]
+        [InlineData("x*(a + b*sin(c + d*(f + x)^n))^2")]
         public void APolynomialBesideAFunctionOfAShiftedLinear(string integrand) => DifferentiatesBack(integrand);
 
         /// <summary>