diff --git a/math/mathcore/src/ProbFuncMathCore.cxx b/math/mathcore/src/ProbFuncMathCore.cxx
index 7ac7d63f0e5e4..201fe10728b0d 100644
--- a/math/mathcore/src/ProbFuncMathCore.cxx
+++ b/math/mathcore/src/ProbFuncMathCore.cxx
@@ -107,7 +107,7 @@ namespace Math {
          MATH_ERROR_MSG("crystalball_integral", "CrystalBall function not defined at alpha=0");
          return 0.;
       }
-      bool useLog = (n == 1.0);
+      bool useLog = (std::abs(n - 1.) < 1.0e-5);
       if (n <= 0)
          MATH_WARN_MSG("crystalball_integral", "No physical meaning when n<=0");
 
@@ -132,11 +132,13 @@ namespace Math {
          double B = r - abs_alpha;
 
          if (!useLog) {
-            intpow = A * (1 - std::pow(r / (B - z), n - 1)) / (n - 1);
+            intpow = A * (1. - std::pow(r / (B - z), n - 1.)) / (n - 1.);
          }
          else {
             // for n=1 the primitive of 1/x is log(x)
-            intpow = A * std::pow(r, n - 1) * (std::log(B - z) - std::log(r));
+            double log_B_z = std::log(B - z);
+            double log_r = std::log(r);
+            intpow = A * std::pow(r, n - 1.) * (log_B_z - log_r + 0.5 * (1. - n) * (log_B_z * log_B_z - log_r * log_r));
          }
          intgaus = sqrtpiover2 * (1. + ROOT::Math::erf(abs_alpha * oneoversqrt2));
       }
diff --git a/roofit/roofit/src/RooCrystalBall.cxx b/roofit/roofit/src/RooCrystalBall.cxx
index bb0dc10722d8c..1a8803003aa68 100644
--- a/roofit/roofit/src/RooCrystalBall.cxx
+++ b/roofit/roofit/src/RooCrystalBall.cxx
@@ -185,7 +185,10 @@ inline double integrateTailLogVersion(double sigma, double alpha, double n, doub
    double a = std::pow(r, n) * exp(-0.5 * alpha * alpha);
    double b = r - alpha;
 
-   return a * sigma * (log(b - tmin) - log(b - tmax));
+   double log_b_tmin = log(b - tmin);
+   double log_b_tmax = log(b - tmax);
+
+   return a * sigma * (log_b_tmin - log_b_tmax + 0.5 * (1.0 - n) * (log_b_tmin * log_b_tmin - log_b_tmax * log_b_tmax));
 }
 
 inline double integrateTailRegular(double sigma, double alpha, double n, double tmin, double tmax)
diff --git a/roofit/roofitcore/inc/RooFit/Detail/MathFuncs.h b/roofit/roofitcore/inc/RooFit/Detail/MathFuncs.h
index a573e5c38ff53..a06933d074c3c 100644
--- a/roofit/roofitcore/inc/RooFit/Detail/MathFuncs.h
+++ b/roofit/roofitcore/inc/RooFit/Detail/MathFuncs.h
@@ -712,7 +712,10 @@ inline double cbShapeIntegral(double mMin, double mMax, double m0, double sigma,
       double b = r - absAlpha;
 
       if (useLog) {
-         result += a * std::pow(r, n - 1) * sig * (std::log(b - tmin) - std::log(b - tmax));
+         double log_b_tmin = std::log(b - tmin);
+         double log_b_tmax = std::log(b - tmax);
+         result += a * std::pow(r, n - 1) * sig *
+                   (log_b_tmin - log_b_tmax + 0.5 * (1.0 - n) * (log_b_tmin * log_b_tmin - log_b_tmax * log_b_tmax));
       } else {
          result += a * sig / (1.0 - n) * (std::pow(r / (b - tmin), n - 1.0) - std::pow(r / (b - tmax), n - 1.0));
       }
@@ -723,7 +726,10 @@ inline double cbShapeIntegral(double mMin, double mMax, double m0, double sigma,
 
       double term1 = 0.0;
       if (useLog) {
-         term1 = a * std::pow(r, n - 1) * sig * (std::log(b - tmin) - std::log(r));
+         double log_b_tmin = std::log(b - tmin);
+         double log_r = std::log(r);
+         term1 = a * std::pow(r, n - 1) * sig *
+                 (log_b_tmin - log_r + 0.5 * (1.0 - n) * (log_b_tmin * log_b_tmin - log_r * log_r));
       } else {
          term1 = a * sig / (1.0 - n) * (std::pow(r / (b - tmin), n - 1.0) - 1.0);
       }