diff --git a/symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/MainTestCase.java b/symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/MainTestCase.java index 3176997e9..4894aaec9 100644 --- a/symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/MainTestCase.java +++ b/symja_android_library/matheclipse-core/src/test/java/org/matheclipse/core/system/MainTestCase.java @@ -1765,190 +1765,6 @@ public void testSystem170() { check("Cross({1, 2, 3}, {a, b, c})", "{-3*b+2*c,3*a-c,-2*a+b}"); } - @Test - public void testSystem171() { - check("N(Integrate(Sin(x),x))", "-Cos(x)"); - check("N(Sin(x))", "Sin(x)"); - check("Cancel((1*x+1/2*2)^((-1)*2)*1^(-1)^(-1))", "1/(1+x)^2"); - check("Integrate(1/(a+b*x),x)", "Log(a+b*x)/b"); - check("Integrate((a+b*x)^(1/3),x)", "3/4*(a+b*x)^(4/3)/b"); - } - - @Test - public void testSystem171a() { - check("Integrate(1/(x^5+x-7),x)", // - "Integrate(1/(-7+x+x^5),x)"); - - check("Rubi`PolyQ(x/(2*Sqrt(2)),x,1)", // - "True"); - check("Rubi`PolyQ((2+2*x)/(2*Sqrt(2)),x)", // - "True"); - // check("Rubi`PolyQ(2+2 *x,x,1)", // - // "True"); - // check("Rubi`PolyQ(-(ArcTan((1+x)/Sqrt(2))/(2 Sqrt(2))),x )", // - // "True"); - check("Rubi`substaux(-ArcTan(x/(2*Sqrt(2)))/(2*Sqrt(2)),x,2+2*x,True)", // - "-ArcTan((1+x)/Sqrt(2))/(2*Sqrt(2))"); - check("Integrate((x^2+2*x+3)^(-1),x)", // - "ArcTan((1+x)/Sqrt(2))/Sqrt(2)"); - - check("Integrate((x-2)^(-3),x)", "-1/(2*(2-x)^2)"); - check("D(-1/(2*(2-x)^2),x)", "-1/(2-x)^3"); - check("Integrate(Log(x)*x^2,x)", // - "-x^3/9+1/3*x^3*Log(x)"); - check("Integrate((x^2+1)*Log(x),x)", // - "1/3*(-3*x-x^3/3)+1/3*(3*x+x^3)*Log(x)"); - check("Simplify(D(ArcTan((2*x-1)*3^(-1/2))*3^(-1/2)+1/6*Log(x^2-x+1)-1/3*Log(x+1),x))", - "x/(1+x^3)"); - - check("Integrate(x/(x^3+1),x)", // - "ArcTan((-1+2*x)/Sqrt(3))/Sqrt(3)-Log(1+x)/3+Log(1-x+x^2)/6"); - // check("Simplify(D(ArcTan((2*x-1)*3^(-1/2))*3^(-1/2)+1/6*Log(x^2-x+1)-1/3*Log(x+1),x))", - // "x*(x^3+1)^(-1)"); - check("Integrate(x*Log(x),x)", // - "-x^2/4+1/2*x^2*Log(x)"); - check("D(-1/2*Log(x)*x^2+3/4*x^2+x*(x*Log(x)-x),x)", // - "x*Log(x)"); - check("integrate(x*Exp(-x^2),x)", "-1/(2*E^x^2)"); - check("D(-Gamma(1,x^2)/2, x)", "x/E^x^2"); - check("Simplify(x*E^(-x^2))", "x/E^x^2"); - - check("Integrate(x^a,x)", "x^(1+a)/(1+a)"); - check("Integrate(a^x,x)", "a^x/Log(a)"); - check("Integrate(x^(-1),x)", "Log(x)"); - check("Integrate(x^a,x)", "x^(1+a)/(1+a)"); - check("Integrate(x^10,x)", "x^11/11"); - check("Simplify(1/2*(2*x+2))", "1+x"); - check("Simplify(1/2*(2*x+2)*(1/2)^(1/2))", // - "(1+x)/Sqrt(2)"); - check("Simplify(Integrate((8*x+1)/(x^2+x+1)^2,x))", // - "-(5+2*x)/(1+x+x^2)+(-4*ArcTan((1+2*x)/Sqrt(3)))/Sqrt(3)"); - - check("Apart(1/(x^3+1))", // - "1/(3*(1+x))+(2-x)/(3*(1-x+x^2))"); - check("Integrate(1/(x^5+x-7),x)", // - "Integrate(1/(-7+x+x^5),x)"); - check("Integrate(1/(x-2),x)", // - "Log(2-x)"); - check("Integrate((x-2)^(-2),x)", // - "1/(2-x)"); - - check("Integrate(1/(x^2+1),x)", // - "ArcTan(x)"); - check("Integrate((2*x+5)/(x^2-2*x+5),x)", // - "7/2*ArcTan(1/2*(-1+x))+Log(5-2*x+x^2)"); - check("Integrate((8*x+1)/(x^2+2*x+1),x)", // - "7/(1+x)+8*Log(1+x)"); - } - - @Test - public void testSystem171b() { - // check("D(2*E^x-Gamma(3,-x),x)", // - // "2*E^x-E^x*x^2"); - - // check("Simplify(Integrate(1/3*(2-x)*(x^2-x+1)^(-1),x))", - // "ArcTan((2*x-1)*3^(-1/2))*3^(-1/2)-1/6*Log(x^2-x+1)"); - check("Integrate(1/3*(2-x)*(x^2-x+1)^(-1)+1/3*(x+1)^(-1),x)", // - "ArcTan((-1+2*x)/Sqrt(3))/Sqrt(3)+Log(1+x)/3-Log(1-x+x^2)/6"); - check("Integrate(E^x*(2-x^2),x)", // - "2*E^x*x-E^x*x^2"); - check("D(2*E^x-Gamma(3,-x),x)", // - "2*E^x-E^x*x^2"); - check("D(-x-Gamma(2,-3*Log(x))/9+x*Log(x),x)", // - "Log(x)+x^2*Log(x)"); - - check("Apart(2*x^2/(x^3+1))", // - "2/3*1/(1+x)+2/3*(-1+2*x)/(1-x+x^2)"); - - check("Integrate(2*x^2/(x^3+1),x)", // - "2/3*Log(1+x^3)"); - check("Integrate(Sin(x)^3,x)", // - "-Cos(x)+Cos(x)^3/3"); - - check("Integrate(Cos(2*x)^3,x)", // - "Sin(2*x)/2-Sin(2*x)^3/6"); - check("Integrate(x,x)", // - "x^2/2"); - check("Integrate(2*x,x)", // - "x^2"); - check("Integrate(h(x),x)", // - "Integrate(h(x),x)"); - check("Integrate(f(x)+g(x)+h(x),x)", // - "Integrate(f(x),x)+Integrate(g(x),x)+Integrate(h(x),x)"); - check("Integrate(Sin(x),x)", // - "-Cos(x)"); - check("Integrate(Sin(10*x),x)", // - "-Cos(10*x)/10"); - check("Integrate(Sin(Pi+10*x),x)", // - "Cos(10*x)/10"); - check("Integrate(E^(a*x),x)", // - "E^(a*x)/a"); - check("Integrate(x*E^(a*x),x)", // - "-E^(a*x)/a^2+(E^(a*x)*x)/a"); - check("Integrate(x*E^x,x)", // - "-E^x+E^x*x"); - check("Integrate(x^2*E^x,x)", // - "2*E^x-2*E^x*x+E^x*x^2"); - check("Integrate(x^2*E^(a*x),x)", // - "(2*E^(a*x))/a^3+(-2*E^(a*x)*x)/a^2+(E^(a*x)*x^2)/a"); - check("Integrate(x^3*E^(a*x),x)", // - "(-6*E^(a*x))/a^4+(6*E^(a*x)*x)/a^3+(-3*E^(a*x)*x^2)/a^2+(E^(a*x)*x^3)/a"); - check("(-1.0)/48", // - "-0.0208333"); - - // to low max points - checkNumeric("NIntegrate(1/(x^2), {x, 1, 1000}, Method->LegendreGauss, MaxPoints->7)", // - "0.1045310822478281"); - checkNumeric("NIntegrate(1/(x^2), {x, 1, 1000}, Method->LegendreGauss, MaxPoints->100)", // - "0.9988852159737875"); - - checkNumeric("NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1),{x,0,1},Method->Trapezoid)", // - "-0.0208333271245165"); - checkNumeric( - "NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1),{x,0,1},Method->Simpson, MaxIterations->10)", // - "NIntegrate((-1+x)*(-0.5+x)*(0.5+x)*x*(1+x),{x,0,1},Method->simpson,MaxIterations->\n" - + "10)"); - checkNumeric("NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1),{x,0,1},Method->Simpson)", // - "-0.0208333320915699"); - - checkNumeric( - "NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1),{x,0,1},Method->Romberg, MaxIterations->10)", // - "-0.0208333333333333"); - checkNumeric("NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1),{x,0,1},Method->Romberg)", // - "-0.0208333333333333"); - checkNumeric("NIntegrate((x-1)*(x-0.5)*x*(x+0.5)*(x+1),{x,0,1})", // - "-0.0208333333333333"); - } - - // @Test - // public void testSystem171c() { - // check("Integrate(ArcCoth(x^16)^2,x)", // - // "1"); - // } - - @Test - public void testSystem172() { - check("Cos((a-b)*x)/(2*(a-b))-Cos((a+b)*x)/(2*(a+b))", // - "Cos((a-b)*x)/(2*(a-b))-Cos((a+b)*x)/(2*(a+b))"); - check("Integrate(Cos(a*x)*Sin(b*x),x)", // - "Cos((a-b)*x)/(2*(a-b))-Cos((a+b)*x)/(2*(a+b))"); - check("Integrate(Cos(a*x)*Sin(b*x),x)", // - "Cos((a-b)*x)/(2*(a-b))-Cos((a+b)*x)/(2*(a+b))"); - - check("Csc(b*x)^0", // - "1"); - check("Integrate(Cos(x*(a+b)),x)", // - "Sin((a+b)*x)/(a+b)"); - // Integrate[Cos[a*x]*Sin[b*x]^2,x] - check("Integrate(Cos(a*x)*Sin(b*x)^2,x)", // - "Sin(a*x)/(2*a)-Sin((a-2*b)*x)/(4*(a-2*b))-Sin((a+2*b)*x)/(4*(a+2*b))"); - check("Integrate(Cos(a*x)^2*Sin(b*x),x)", // - "Cos((2*a-b)*x)/(4*(2*a-b))-Cos(b*x)/(2*b)-Cos((2*a+b)*x)/(4*(2*a+b))"); - check("Integrate(Cos(b*x)^2*Sin(a*x)^2,x)", // - "x/4-Sin(2*a*x)/(8*a)-Sin(2*(a-b)*x)/(16*(a-b))+Sin(2*b*x)/(8*b)-Sin(2*(a+b)*x)/(\n" - + "16*(a+b))"); - } - @Test public void testSystem173() { check("N(1.0)", "1.0");