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#149 generated Integrate sources
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‎symja_android_library/matheclipse-core/src/main/java/org/matheclipse/core/integrate/rubi/IntRules0.java

Lines changed: 0 additions & 50 deletions
Original file line numberDiff line numberDiff line change
@@ -70,56 +70,6 @@ private static void init() {
7070
Condition(Dist(Power(b,CN2),Int(Times(u,Power(Plus(a,Times(b,v)),Plus(m,C1)),Simp(Plus(Times(b,BSymbol),Times(CN1,a,C),Times(b,C,v)),x)),x),x),And(FreeQ(List(a,b,ASymbol,BSymbol,C),x),EqQ(Plus(Times(ASymbol,Sqr(b)),Times(CN1,a,b,BSymbol),Times(Sqr(a),C)),C0),LeQ(m,CN1))));
7171
IIntegrate(25,Int(Times(u_DEFAULT,Power(Plus(a_,Times(b_DEFAULT,Power(x_,n_DEFAULT))),m_DEFAULT),Power(Plus(c_,Times(d_DEFAULT,Power(x_,q_DEFAULT))),p_DEFAULT)),x_Symbol),
7272
Condition(Dist(Power(Times(d,Power(a,CN1)),p),Int(Times(u,Power(Plus(a,Times(b,Power(x,n))),Plus(m,p)),Power(Power(x,Times(n,p)),CN1)),x),x),And(FreeQ(List(a,b,c,d,m,n),x),EqQ(q,Negate(n)),IntegerQ(p),EqQ(Subtract(Times(a,c),Times(b,d)),C0),Not(And(IntegerQ(m),NegQ(n))))));
73-
IIntegrate(26,Int(Times(u_DEFAULT,Power(Plus(a_,Times(b_DEFAULT,Power(x_,n_DEFAULT))),m_DEFAULT),Power(Plus(c_,Times(d_DEFAULT,Power(x_,j_))),p_DEFAULT)),x_Symbol),
74-
Condition(Dist(Power(Times(CN1,Sqr(b),Power(d,CN1)),m),Int(Times(u,Power(Power(Subtract(a,Times(b,Power(x,n))),m),CN1)),x),x),And(FreeQ(List(a,b,c,d,m,n,p),x),EqQ(j,Times(C2,n)),EqQ(p,Negate(m)),EqQ(Plus(Times(Sqr(b),c),Times(Sqr(a),d)),C0),GtQ(a,C0),LtQ(d,C0))));
75-
IIntegrate(27,Int(Times(u_DEFAULT,Power(Plus(a_,Times(b_DEFAULT,x_),Times(c_DEFAULT,Sqr(x_))),p_DEFAULT)),x_Symbol),
76-
Condition(Int(Times(u,Cancel(Times(Power(Plus(Times(C1D2,b),Times(c,x)),Times(C2,p)),Power(Power(c,p),CN1)))),x),And(FreeQ(List(a,b,c),x),EqQ(Subtract(Sqr(b),Times(C4,a,c)),C0),IntegerQ(p))));
77-
IIntegrate(28,Int(Times(u_DEFAULT,Power(Plus(a_,Times(c_DEFAULT,Power(x_,$p("n2",true))),Times(b_DEFAULT,Power(x_,n_))),p_DEFAULT)),x_Symbol),
78-
Condition(Dist(Power(Power(c,p),CN1),Int(Times(u,Power(Plus(Times(C1D2,b),Times(c,Power(x,n))),Times(C2,p))),x),x),And(FreeQ(List(a,b,c,n),x),EqQ($s("n2"),Times(C2,n)),EqQ(Subtract(Sqr(b),Times(C4,a,c)),C0),IntegerQ(p))));
79-
IIntegrate(29,Int(Power(x_,CN1),x_Symbol),
80-
Simp(Log(x),x));
81-
IIntegrate(30,Int(Power(x_,m_DEFAULT),x_Symbol),
82-
Condition(Simp(Times(Power(x,Plus(m,C1)),Power(Plus(m,C1),CN1)),x),And(FreeQ(m,x),NeQ(m,CN1))));
83-
IIntegrate(31,Int(Power(Plus(a_,Times(b_DEFAULT,x_)),CN1),x_Symbol),
84-
Condition(Simp(Times(Log(RemoveContent(Plus(a,Times(b,x)),x)),Power(b,CN1)),x),FreeQ(List(a,b),x)));
85-
IIntegrate(32,Int(Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_)),m_),x_Symbol),
86-
Condition(Simp(Times(Power(Plus(a,Times(b,x)),Plus(m,C1)),Power(Times(b,Plus(m,C1)),CN1)),x),And(FreeQ(List(a,b,m),x),NeQ(m,CN1))));
87-
IIntegrate(33,Int(Power(Plus(a_DEFAULT,Times(b_DEFAULT,u_)),m_),x_Symbol),
88-
Condition(Dist(Power(Coefficient(u,x,C1),CN1),Subst(Int(Power(Plus(a,Times(b,x)),m),x),x,u),x),And(FreeQ(List(a,b,m),x),LinearQ(u,x),NeQ(u,x))));
89-
IIntegrate(34,Int(Times(Power(Plus(a_,Times(b_DEFAULT,x_)),m_DEFAULT),Plus(c_,Times(d_DEFAULT,x_))),x_Symbol),
90-
Condition(Simp(Times(d,x,Power(Plus(a,Times(b,x)),Plus(m,C1)),Power(Times(b,Plus(m,C2)),CN1)),x),And(FreeQ(List(a,b,c,d,m),x),EqQ(Subtract(Times(a,d),Times(b,c,Plus(m,C2))),C0))));
91-
IIntegrate(35,Int(Times(Power(Plus(a_,Times(b_DEFAULT,x_)),CN1),Power(Plus(c_,Times(d_DEFAULT,x_)),CN1)),x_Symbol),
92-
Condition(Int(Power(Plus(Times(a,c),Times(b,d,Sqr(x))),CN1),x),And(FreeQ(List(a,b,c,d),x),EqQ(Plus(Times(b,c),Times(a,d)),C0))));
93-
IIntegrate(36,Int(Times(Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_)),CN1),Power(Plus(c_DEFAULT,Times(d_DEFAULT,x_)),CN1)),x_Symbol),
94-
Condition(Subtract(Dist(Times(b,Power(Subtract(Times(b,c),Times(a,d)),CN1)),Int(Power(Plus(a,Times(b,x)),CN1),x),x),Dist(Times(d,Power(Subtract(Times(b,c),Times(a,d)),CN1)),Int(Power(Plus(c,Times(d,x)),CN1),x),x)),And(FreeQ(List(a,b,c,d),x),NeQ(Subtract(Times(b,c),Times(a,d)),C0))));
95-
IIntegrate(37,Int(Times(Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_)),m_DEFAULT),Power(Plus(c_DEFAULT,Times(d_DEFAULT,x_)),n_)),x_Symbol),
96-
Condition(Simp(Times(Power(Plus(a,Times(b,x)),Plus(m,C1)),Power(Plus(c,Times(d,x)),Plus(n,C1)),Power(Times(Subtract(Times(b,c),Times(a,d)),Plus(m,C1)),CN1)),x),And(FreeQ(List(a,b,c,d,m,n),x),NeQ(Subtract(Times(b,c),Times(a,d)),C0),EqQ(Plus(m,n,C2),C0),NeQ(m,CN1))));
97-
IIntegrate(38,Int(Times(Power(Plus(a_,Times(b_DEFAULT,x_)),m_),Power(Plus(c_,Times(d_DEFAULT,x_)),m_)),x_Symbol),
98-
Condition(Plus(Simp(Times(x,Power(Plus(a,Times(b,x)),m),Power(Plus(c,Times(d,x)),m),Power(Plus(Times(C2,m),C1),CN1)),x),Dist(Times(C2,a,c,m,Power(Plus(Times(C2,m),C1),CN1)),Int(Times(Power(Plus(a,Times(b,x)),Subtract(m,C1)),Power(Plus(c,Times(d,x)),Subtract(m,C1))),x),x)),And(FreeQ(List(a,b,c,d),x),EqQ(Plus(Times(b,c),Times(a,d)),C0),IGtQ(Plus(m,C1D2),C0))));
99-
IIntegrate(39,Int(Times(Power(Plus(a_,Times(b_DEFAULT,x_)),QQ(-3L,2L)),Power(Plus(c_,Times(d_DEFAULT,x_)),QQ(-3L,2L))),x_Symbol),
100-
Condition(Simp(Times(x,Power(Times(a,c,Sqrt(Plus(a,Times(b,x))),Sqrt(Plus(c,Times(d,x)))),CN1)),x),And(FreeQ(List(a,b,c,d),x),EqQ(Plus(Times(b,c),Times(a,d)),C0))));
101-
IIntegrate(40,Int(Times(Power(Plus(a_,Times(b_DEFAULT,x_)),m_),Power(Plus(c_,Times(d_DEFAULT,x_)),m_)),x_Symbol),
102-
Condition(Plus(Negate(Simp(Times(x,Power(Plus(a,Times(b,x)),Plus(m,C1)),Power(Plus(c,Times(d,x)),Plus(m,C1)),Power(Times(C2,a,c,Plus(m,C1)),CN1)),x)),Dist(Times(Plus(Times(C2,m),C3),Power(Times(C2,a,c,Plus(m,C1)),CN1)),Int(Times(Power(Plus(a,Times(b,x)),Plus(m,C1)),Power(Plus(c,Times(d,x)),Plus(m,C1))),x),x)),And(FreeQ(List(a,b,c,d),x),EqQ(Plus(Times(b,c),Times(a,d)),C0),ILtQ(Plus(m,QQ(3L,2L)),C0))));
103-
IIntegrate(41,Int(Times(Power(Plus(a_,Times(b_DEFAULT,x_)),m_DEFAULT),Power(Plus(c_,Times(d_DEFAULT,x_)),m_DEFAULT)),x_Symbol),
104-
Condition(Int(Power(Plus(Times(a,c),Times(b,d,Sqr(x))),m),x),And(FreeQ(List(a,b,c,d,m),x),EqQ(Plus(Times(b,c),Times(a,d)),C0),Or(IntegerQ(m),And(GtQ(a,C0),GtQ(c,C0))))));
105-
IIntegrate(42,Int(Times(Power(Plus(a_,Times(b_DEFAULT,x_)),m_),Power(Plus(c_,Times(d_DEFAULT,x_)),m_)),x_Symbol),
106-
Condition(Dist(Times(Power(Plus(a,Times(b,x)),FracPart(m)),Power(Plus(c,Times(d,x)),FracPart(m)),Power(Power(Plus(Times(a,c),Times(b,d,Sqr(x))),FracPart(m)),CN1)),Int(Power(Plus(Times(a,c),Times(b,d,Sqr(x))),m),x),x),And(FreeQ(List(a,b,c,d,m),x),EqQ(Plus(Times(b,c),Times(a,d)),C0),Not(IntegerQ(Times(C2,m))))));
107-
IIntegrate(43,Int(Times(Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_)),m_DEFAULT),Power(Plus(c_DEFAULT,Times(d_DEFAULT,x_)),n_DEFAULT)),x_Symbol),
108-
Condition(Int(ExpandIntegrand(Times(Power(Plus(a,Times(b,x)),m),Power(Plus(c,Times(d,x)),n)),x),x),And(FreeQ(List(a,b,c,d,n),x),NeQ(Subtract(Times(b,c),Times(a,d)),C0),IGtQ(m,C0),Or(Not(IntegerQ(n)),And(EqQ(c,C0),LeQ(Plus(Times(C7,m),Times(C4,n),C4),C0)),LtQ(Plus(Times(C9,m),Times(C5,Plus(n,C1))),C0),GtQ(Plus(m,n,C2),C0)))));
109-
IIntegrate(44,Int(Times(Power(Plus(a_,Times(b_DEFAULT,x_)),m_DEFAULT),Power(Plus(c_DEFAULT,Times(d_DEFAULT,x_)),n_DEFAULT)),x_Symbol),
110-
Condition(Int(ExpandIntegrand(Times(Power(Plus(a,Times(b,x)),m),Power(Plus(c,Times(d,x)),n)),x),x),And(FreeQ(List(a,b,c,d),x),NeQ(Subtract(Times(b,c),Times(a,d)),C0),ILtQ(m,C0),IntegerQ(n),Not(And(IGtQ(n,C0),LtQ(Plus(m,n,C2),C0))))));
111-
IIntegrate(45,Int(Times(Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_)),m_),Power(Plus(c_DEFAULT,Times(d_DEFAULT,x_)),n_)),x_Symbol),
112-
Condition(Subtract(Simp(Times(Power(Plus(a,Times(b,x)),Plus(m,C1)),Power(Plus(c,Times(d,x)),Plus(n,C1)),Power(Times(Subtract(Times(b,c),Times(a,d)),Plus(m,C1)),CN1)),x),Dist(Times(d,Simplify(Plus(m,n,C2)),Power(Times(Subtract(Times(b,c),Times(a,d)),Plus(m,C1)),CN1)),Int(Times(Power(Plus(a,Times(b,x)),Simplify(Plus(m,C1))),Power(Plus(c,Times(d,x)),n)),x),x)),And(FreeQ(List(a,b,c,d,m,n),x),NeQ(Subtract(Times(b,c),Times(a,d)),C0),ILtQ(Simplify(Plus(m,n,C2)),C0),NeQ(m,CN1),Not(And(LtQ(m,CN1),LtQ(n,CN1),Or(EqQ(a,C0),And(NeQ(c,C0),LtQ(Subtract(m,n),C0),IntegerQ(n))))),Or(SumSimplerQ(m,C1),Not(SumSimplerQ(n,C1))))));
113-
IIntegrate(46,Int(Times(Power(Plus(a_,Times(b_DEFAULT,x_)),QQ(-9L,4L)),Power(Plus(c_,Times(d_DEFAULT,x_)),CN1D4)),x_Symbol),
114-
Condition(Subtract(Simp(Times(CN4,Power(Times(C5,b,Power(Plus(a,Times(b,x)),QQ(5L,4L)),Power(Plus(c,Times(d,x)),C1D4)),CN1)),x),Dist(Times(d,Power(Times(C5,b),CN1)),Int(Power(Times(Power(Plus(a,Times(b,x)),QQ(5L,4L)),Power(Plus(c,Times(d,x)),QQ(5L,4L))),CN1),x),x)),And(FreeQ(List(a,b,c,d),x),EqQ(Plus(Times(b,c),Times(a,d)),C0),NegQ(Times(Sqr(a),Sqr(b))))));
115-
IIntegrate(47,Int(Times(Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_)),m_),Power(Plus(c_DEFAULT,Times(d_DEFAULT,x_)),n_)),x_Symbol),
116-
Condition(Subtract(Simp(Times(Power(Plus(a,Times(b,x)),Plus(m,C1)),Power(Plus(c,Times(d,x)),n),Power(Times(b,Plus(m,C1)),CN1)),x),Dist(Times(d,n,Power(Times(b,Plus(m,C1)),CN1)),Int(Times(Power(Plus(a,Times(b,x)),Plus(m,C1)),Power(Plus(c,Times(d,x)),Subtract(n,C1))),x),x)),And(FreeQ(List(a,b,c,d),x),NeQ(Subtract(Times(b,c),Times(a,d)),C0),GtQ(n,C0),LtQ(m,CN1),Not(And(IntegerQ(n),Not(IntegerQ(m)))),Not(And(ILeQ(Plus(m,n,C2),C0),Or(FractionQ(m),GeQ(Plus(Times(C2,n),m,C1),C0)))),IntLinearQ(a,b,c,d,m,n,x))));
117-
IIntegrate(48,Int(Times(Power(Plus(a_,Times(b_DEFAULT,x_)),QQ(-5L,4L)),Power(Plus(c_,Times(d_DEFAULT,x_)),CN1D4)),x_Symbol),
118-
Condition(Plus(Simp(Times(CN2,Power(Times(b,Power(Plus(a,Times(b,x)),C1D4),Power(Plus(c,Times(d,x)),C1D4)),CN1)),x),Dist(c,Int(Power(Times(Power(Plus(a,Times(b,x)),QQ(5L,4L)),Power(Plus(c,Times(d,x)),QQ(5L,4L))),CN1),x),x)),And(FreeQ(List(a,b,c,d),x),EqQ(Plus(Times(b,c),Times(a,d)),C0),NegQ(Times(Sqr(a),Sqr(b))))));
119-
IIntegrate(49,Int(Times(Power(Plus(a_,Times(b_DEFAULT,x_)),m_),Power(Plus(c_,Times(d_DEFAULT,x_)),n_)),x_Symbol),
120-
Condition(Plus(Simp(Times(Power(Plus(a,Times(b,x)),Plus(m,C1)),Power(Plus(c,Times(d,x)),n),Power(Times(b,Plus(m,n,C1)),CN1)),x),Dist(Times(C2,c,n,Power(Plus(m,n,C1),CN1)),Int(Times(Power(Plus(a,Times(b,x)),m),Power(Plus(c,Times(d,x)),Subtract(n,C1))),x),x)),And(FreeQ(List(a,b,c,d),x),EqQ(Plus(Times(b,c),Times(a,d)),C0),IGtQ(Plus(m,C1D2),C0),IGtQ(Plus(n,C1D2),C0),LtQ(m,n))));
121-
IIntegrate(50,Int(Times(Power(Plus(a_DEFAULT,Times(b_DEFAULT,x_)),m_),Power(Plus(c_DEFAULT,Times(d_DEFAULT,x_)),n_)),x_Symbol),
122-
Condition(Plus(Simp(Times(Power(Plus(a,Times(b,x)),Plus(m,C1)),Power(Plus(c,Times(d,x)),n),Power(Times(b,Plus(m,n,C1)),CN1)),x),Dist(Times(n,Subtract(Times(b,c),Times(a,d)),Power(Times(b,Plus(m,n,C1)),CN1)),Int(Times(Power(Plus(a,Times(b,x)),m),Power(Plus(c,Times(d,x)),Subtract(n,C1))),x),x)),And(FreeQ(List(a,b,c,d),x),NeQ(Subtract(Times(b,c),Times(a,d)),C0),GtQ(n,C0),NeQ(Plus(m,n,C1),C0),Not(And(IGtQ(m,C0),Or(Not(IntegerQ(n)),And(GtQ(m,C0),LtQ(Subtract(m,n),C0))))),Not(ILtQ(Plus(m,n,C2),C0)),IntLinearQ(a,b,c,d,m,n,x))));
12373
}
12474
}
12575
}

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