stopgap patch to fix issues with integrating simple rational functions

Task #139 - simple rational function integral not calculated
grzegorzmazur · Oct 12, 2015 · 4466691 · 4466691
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commit 4466691
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diff --git a/scripts/integrate.rep/code.ys b/scripts/integrate.rep/code.ys
@@ -178,6 +178,31 @@ UnFence("IntegrateMultiplicative",4);
   `AntiDeriv(@var,@ee);
 ];
 
+15 # IntRat(_var,_exy / _exx,_exyu,_exxu)_
+        (Degree(exyu, var) = 0 And Degree(exxu, var) = 2 And
+         IsNumericList(Coef(exxu,var,0 .. Degree(exxu))) And
+         IsNumericList(Coef(exyu,var,0 .. Degree(exyu)))) <-- [
+    Local(a,b,c,d,e,delta);
+    {d} := Coef(exyu, var, 0 .. 0);
+    {c, b, a} := Coef(exxu, var, 0 .. 2);
+
+    delta := b^2-4*a*c;
+
+    2 * d / Sqrt(-delta) * ArcTan((2*a*var+b) / Sqrt(-delta));
+];
+
+15 # IntRat(_var,_exy / _exx,_exyu,_exxu)_
+        (Degree(exyu, var) = 1 And Degree(exxu, var) = 2 And
+         IsNumericList(Coef(exxu,var,0 .. Degree(exxu))) And
+         IsNumericList(Coef(exyu,var,0 .. Degree(exyu)))) <-- [
+    Local(a,b,c,d,e,r);
+    {e, d} := Coef(exyu, var, 0 .. 1);
+    {c, b, a} := Coef(exxu, var, 0 .. 2);
+
+    r := (e - b * d / (2 * a)) / exx;
+
+    d / (2 * a) * Ln(exx) + `AntiDeriv(@var, @r);
+];
 
 20 # IntRat(_var,_exy / _exx,_exyu,_exxu) <--
      `Hold(AntiDeriv(@var,((@exy)/(@exx))));

diff --git a/tests/integrate.yts b/tests/integrate.yts
@@ -22,6 +22,8 @@ Verify(Integrate(x) (x + 4)/(x + 3)^2, Ln(x+3)-(x+3)^(-1));
 Verify(Integrate(x) 1/(4 * x^2 + 1), ArcTan(2*x)/2);
 Verify(Integrate(x) (x-1)/(x^2-1), Ln(x+1));
 
+Verify(Integrate(x) x/(x^3+1), Ln(3*(1-x+x^2))/6+Sqrt(1/3)*ArcTan((4*x-2)/Sqrt(12))-Ln(3*(x+1))/3);
+
 Verify(Integrate(x) 3/Sin(x),3*Ln(1/Sin(x)-Cos(x)/Sin(x)) );
 
 Verify(Integrate(x) Ln(x), x*Ln(x)-x );