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Delete Integrate tests from MainTestCase
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- move to `IntegrateTest` later
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@axkr
axkr committed Sep 5, 2024
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184 changes: 0 additions & 184 deletions ...roid_library/matheclipse-core/src/test/java/org/matheclipse/core/system/MainTestCase.java
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Original file line number Diff line number Diff line change
Expand Up @@ -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");
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