1,0,0,189,0.2974166,"\int (e x)^m \left(a+b x^2\right)^3 \left(A+B x^2\right) \left(c+d x^2\right) \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x^2)^3*(A + B*x^2)*(c + d*x^2),x]","\int (e x)^m \left(a+b x^2\right)^3 \left(A+B x^2\right) \left(c+d x^2\right) \, dx","\frac{a^3 A c (e x)^{m+1}}{e (m+1)}+\frac{a^2 (e x)^{m+3} (a A d+a B c+3 A b c)}{e^3 (m+3)}+\frac{b^2 (e x)^{m+9} (3 a B d+A b d+b B c)}{e^9 (m+9)}+\frac{b (e x)^{m+7} (A b (3 a d+b c)+3 a B (a d+b c))}{e^7 (m+7)}+\frac{a (e x)^{m+5} (3 A b (a d+b c)+a B (a d+3 b c))}{e^5 (m+5)}+\frac{b^3 B d (e x)^{m+11}}{e^{11} (m+11)}",1,"Could not integrate","F",-1
2,0,0,144,0.0458154,"\int (e x)^m \left(a+b x^2\right)^2 \left(A+B x^2\right) \left(c+d x^2\right) \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x^2)^2*(A + B*x^2)*(c + d*x^2),x]","\int (e x)^m \left(a+b x^2\right)^2 \left(A+B x^2\right) \left(c+d x^2\right) \, dx","\frac{a^2 A c (e x)^{m+1}}{e (m+1)}+\frac{b (e x)^{m+7} (2 a B d+A b d+b B c)}{e^7 (m+7)}+\frac{(e x)^{m+5} (A b (2 a d+b c)+a B (a d+2 b c))}{e^5 (m+5)}+\frac{a (e x)^{m+3} (a A d+a B c+2 A b c)}{e^3 (m+3)}+\frac{b^2 B d (e x)^{m+9}}{e^9 (m+9)}",1,"Could not integrate","F",-1
3,0,0,97,0.0239593,"\int (e x)^m \left(a+b x^2\right) \left(A+B x^2\right) \left(c+d x^2\right) \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x^2)*(A + B*x^2)*(c + d*x^2),x]","\int (e x)^m \left(a+b x^2\right) \left(A+B x^2\right) \left(c+d x^2\right) \, dx","\frac{(e x)^{m+5} (a B d+A b d+b B c)}{e^5 (m+5)}+\frac{(e x)^{m+3} (a A d+a B c+A b c)}{e^3 (m+3)}+\frac{a A c (e x)^{m+1}}{e (m+1)}+\frac{b B d (e x)^{m+7}}{e^7 (m+7)}",1,"Could not integrate","F",-1
4,0,0,60,0.0147322,"\int (e x)^m \left(A+B x^2\right) \left(c+d x^2\right) \, dx","IntegrateAlgebraic[(e*x)^m*(A + B*x^2)*(c + d*x^2),x]","\int (e x)^m \left(A+B x^2\right) \left(c+d x^2\right) \, dx","\frac{(e x)^{m+3} (A d+B c)}{e^3 (m+3)}+\frac{A c (e x)^{m+1}}{e (m+1)}+\frac{B d (e x)^{m+5}}{e^5 (m+5)}",1,"Could not integrate","F",-1
5,0,0,118,0.0445946,"\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)}{a+b x^2} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2)*(c + d*x^2))/(a + b*x^2),x]","\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)}{a+b x^2} \, dx","\frac{(e x)^{m+1} (A b-a B) (b c-a d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b^2 e (m+1)}+\frac{(e x)^{m+1} (-a B d+A b d+b B c)}{b^2 e (m+1)}+\frac{B d (e x)^{m+3}}{b e^3 (m+3)}",1,"Could not integrate","F",-1
6,0,0,171,0.163697,"\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2)*(c + d*x^2))/(a + b*x^2)^2,x]","\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)}{\left(a+b x^2\right)^2} \, dx","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right) (A b (a d (m+1)+b (c-c m))+a B (b c (m+1)-a d (m+3)))}{2 a^2 b^2 e (m+1)}-\frac{d (e x)^{m+1} (A b (m+1)-a B (m+3))}{2 a b^2 e (m+1)}+\frac{\left(c+d x^2\right) (e x)^{m+1} (A b-a B)}{2 a b e \left(a+b x^2\right)}",1,"Could not integrate","F",-1
7,0,0,209,0.3326616,"\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2)*(c + d*x^2))/(a + b*x^2)^3,x]","\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)}{\left(a+b x^2\right)^3} \, dx","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right) (A b (1-m) (a d (m+1)+b c (3-m))+a B (m+1) (a d (m+3)+b (c-c m)))}{8 a^3 b^2 e (m+1)}-\frac{(e x)^{m+1} (A b (a d (1-m)-b c (3-m))-a B (b c (m+1)-a d (m+3)))}{8 a^2 b^2 e \left(a+b x^2\right)}+\frac{\left(c+d x^2\right) (e x)^{m+1} (A b-a B)}{4 a b e \left(a+b x^2\right)^2}",1,"Could not integrate","F",-1
8,0,0,292,0.493625,"\int (e x)^m \left(a+b x^2\right)^3 \left(A+B x^2\right) \left(c+d x^2\right)^2 \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x^2)^3*(A + B*x^2)*(c + d*x^2)^2,x]","\int (e x)^m \left(a+b x^2\right)^3 \left(A+B x^2\right) \left(c+d x^2\right)^2 \, dx","\frac{a^3 A c^2 (e x)^{m+1}}{e (m+1)}+\frac{(e x)^{m+7} \left(A b \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a B \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)\right)}{e^7 (m+7)}+\frac{a (e x)^{m+5} \left(A \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+a B c (2 a d+3 b c)\right)}{e^5 (m+5)}+\frac{b (e x)^{m+9} \left(3 a^2 B d^2+3 a b d (A d+2 B c)+b^2 c (2 A d+B c)\right)}{e^9 (m+9)}+\frac{a^2 c (e x)^{m+3} (2 a A d+a B c+3 A b c)}{e^3 (m+3)}+\frac{b^2 d (e x)^{m+11} (3 a B d+A b d+2 b B c)}{e^{11} (m+11)}+\frac{b^3 B d^2 (e x)^{m+13}}{e^{13} (m+13)}",1,"Could not integrate","F",-1
9,0,0,216,0.132248,"\int (e x)^m \left(a+b x^2\right)^2 \left(A+B x^2\right) \left(c+d x^2\right)^2 \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x^2)^2*(A + B*x^2)*(c + d*x^2)^2,x]","\int (e x)^m \left(a+b x^2\right)^2 \left(A+B x^2\right) \left(c+d x^2\right)^2 \, dx","\frac{(e x)^{m+5} \left(A \left(a^2 d^2+4 a b c d+b^2 c^2\right)+2 a B c (a d+b c)\right)}{e^5 (m+5)}+\frac{(e x)^{m+7} \left(a^2 B d^2+2 a b d (A d+2 B c)+b^2 c (2 A d+B c)\right)}{e^7 (m+7)}+\frac{a^2 A c^2 (e x)^{m+1}}{e (m+1)}+\frac{b d (e x)^{m+9} (2 a B d+A b d+2 b B c)}{e^9 (m+9)}+\frac{a c (e x)^{m+3} (2 A (a d+b c)+a B c)}{e^3 (m+3)}+\frac{b^2 B d^2 (e x)^{m+11}}{e^{11} (m+11)}",1,"Could not integrate","F",-1
10,0,0,144,0.0448363,"\int (e x)^m \left(a+b x^2\right) \left(A+B x^2\right) \left(c+d x^2\right)^2 \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x^2)*(A + B*x^2)*(c + d*x^2)^2,x]","\int (e x)^m \left(a+b x^2\right) \left(A+B x^2\right) \left(c+d x^2\right)^2 \, dx","\frac{d (e x)^{m+7} (a B d+A b d+2 b B c)}{e^7 (m+7)}+\frac{(e x)^{m+5} (a d (A d+2 B c)+b c (2 A d+B c))}{e^5 (m+5)}+\frac{c (e x)^{m+3} (2 a A d+a B c+A b c)}{e^3 (m+3)}+\frac{a A c^2 (e x)^{m+1}}{e (m+1)}+\frac{b B d^2 (e x)^{m+9}}{e^9 (m+9)}",1,"Could not integrate","F",-1
11,0,0,91,0.0219728,"\int (e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^2 \, dx","IntegrateAlgebraic[(e*x)^m*(A + B*x^2)*(c + d*x^2)^2,x]","\int (e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^2 \, dx","\frac{d (e x)^{m+5} (A d+2 B c)}{e^5 (m+5)}+\frac{c (e x)^{m+3} (2 A d+B c)}{e^3 (m+3)}+\frac{A c^2 (e x)^{m+1}}{e (m+1)}+\frac{B d^2 (e x)^{m+7}}{e^7 (m+7)}",1,"Could not integrate","F",-1
12,0,0,178,0.4159086,"\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^2}{a+b x^2} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2)*(c + d*x^2)^2)/(a + b*x^2),x]","\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^2}{a+b x^2} \, dx","\frac{(e x)^{m+1} \left(a^2 B d^2-a b d (A d+2 B c)+b^2 c (2 A d+B c)\right)}{b^3 e (m+1)}+\frac{(e x)^{m+1} (A b-a B) (b c-a d)^2 \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b^3 e (m+1)}+\frac{d (e x)^{m+3} (-a B d+A b d+2 b B c)}{b^2 e^3 (m+3)}+\frac{B d^2 (e x)^{m+5}}{b e^5 (m+5)}",1,"Could not integrate","F",-1
13,0,0,247,0.5634129,"\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^2}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2)*(c + d*x^2)^2)/(a + b*x^2)^2,x]","\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^2}{\left(a+b x^2\right)^2} \, dx","\frac{(e x)^{m+1} (b c-a d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right) (A b (a d (m+3)+b (c-c m))+a B (b c (m+1)-a d (m+5)))}{2 a^2 b^3 e (m+1)}-\frac{d (e x)^{m+1} (A b (2 b c (m+1)-a d (m+3))-a B (2 b c (m+3)-a d (m+5)))}{2 a b^3 e (m+1)}-\frac{d^2 (e x)^{m+3} (A b (m+3)-a B (m+5))}{2 a b^2 e^3 (m+3)}+\frac{\left(c+d x^2\right)^2 (e x)^{m+1} (A b-a B)}{2 a b e \left(a+b x^2\right)}",1,"Could not integrate","F",-1
14,0,0,292,0.738691,"\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^2}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2)*(c + d*x^2)^2)/(a + b*x^2)^3,x]","\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^2}{\left(a+b x^2\right)^3} \, dx","-\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right) (a d (A b (m+1)-a B (m+5)) (b c (m+1)-a d (m+3))-b c (a B (m+1)+A b (3-m)) (a d (m+1)+b (c-c m)))}{8 a^3 b^3 e (m+1)}+\frac{d (e x)^{m+1} (A b (m+1)-a B (m+5)) (b c (m+1)-a d (m+3))}{8 a^2 b^3 e (m+1)}+\frac{(e x)^{m+1} (b c-a d) \left(c (a B (m+1)+A b (3-m))-d x^2 (A b (m+1)-a B (m+5))\right)}{8 a^2 b^2 e \left(a+b x^2\right)}+\frac{\left(c+d x^2\right)^2 (e x)^{m+1} (A b-a B)}{4 a b e \left(a+b x^2\right)^2}",1,"Could not integrate","F",-1
15,0,0,379,0.5681692,"\int (e x)^m \left(a+b x^2\right)^3 \left(A+B x^2\right) \left(c+d x^2\right)^3 \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x^2)^3*(A + B*x^2)*(c + d*x^2)^3,x]","\int (e x)^m \left(a+b x^2\right)^3 \left(A+B x^2\right) \left(c+d x^2\right)^3 \, dx","\frac{a^3 A c^3 (e x)^{m+1}}{e (m+1)}+\frac{3 a c (e x)^{m+5} \left(A \left(a^2 d^2+3 a b c d+b^2 c^2\right)+a B c (a d+b c)\right)}{e^5 (m+5)}+\frac{3 b d (e x)^{m+11} \left(a^2 B d^2+a b d (A d+3 B c)+b^2 c (A d+B c)\right)}{e^{11} (m+11)}+\frac{a^2 c^2 (e x)^{m+3} (3 A (a d+b c)+a B c)}{e^3 (m+3)}+\frac{(e x)^{m+9} \left(a^3 B d^3+3 a^2 b d^2 (A d+3 B c)+9 a b^2 c d (A d+B c)+b^3 c^2 (3 A d+B c)\right)}{e^9 (m+9)}+\frac{(e x)^{m+7} \left(3 a B c \left(a^2 d^2+3 a b c d+b^2 c^2\right)+A \left(a^3 d^3+9 a^2 b c d^2+9 a b^2 c^2 d+b^3 c^3\right)\right)}{e^7 (m+7)}+\frac{b^2 d^2 (e x)^{m+13} (3 a B d+A b d+3 b B c)}{e^{13} (m+13)}+\frac{b^3 B d^3 (e x)^{m+15}}{e^{15} (m+15)}",1,"Could not integrate","F",-1
16,0,0,284,0.5558267,"\int (e x)^m \left(a+b x^2\right)^2 \left(A+B x^2\right) \left(c+d x^2\right)^3 \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x^2)^2*(A + B*x^2)*(c + d*x^2)^3,x]","\int (e x)^m \left(a+b x^2\right)^2 \left(A+B x^2\right) \left(c+d x^2\right)^3 \, dx","\frac{(e x)^{m+7} \left(a^2 d^2 (A d+3 B c)+6 a b c d (A d+B c)+b^2 c^2 (3 A d+B c)\right)}{e^7 (m+7)}+\frac{c (e x)^{m+5} \left(A \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a B c (3 a d+2 b c)\right)}{e^5 (m+5)}+\frac{d (e x)^{m+9} \left(a^2 B d^2+2 a b d (A d+3 B c)+3 b^2 c (A d+B c)\right)}{e^9 (m+9)}+\frac{a^2 A c^3 (e x)^{m+1}}{e (m+1)}+\frac{a c^2 (e x)^{m+3} (3 a A d+a B c+2 A b c)}{e^3 (m+3)}+\frac{b d^2 (e x)^{m+11} (2 a B d+A b d+3 b B c)}{e^{11} (m+11)}+\frac{b^2 B d^3 (e x)^{m+13}}{e^{13} (m+13)}",1,"Could not integrate","F",-1
17,0,0,189,0.2939975,"\int (e x)^m \left(a+b x^2\right) \left(A+B x^2\right) \left(c+d x^2\right)^3 \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x^2)*(A + B*x^2)*(c + d*x^2)^3,x]","\int (e x)^m \left(a+b x^2\right) \left(A+B x^2\right) \left(c+d x^2\right)^3 \, dx","\frac{c^2 (e x)^{m+3} (3 a A d+a B c+A b c)}{e^3 (m+3)}+\frac{d^2 (e x)^{m+9} (a B d+A b d+3 b B c)}{e^9 (m+9)}+\frac{d (e x)^{m+7} (a d (A d+3 B c)+3 b c (A d+B c))}{e^7 (m+7)}+\frac{c (e x)^{m+5} (3 a d (A d+B c)+b c (3 A d+B c))}{e^5 (m+5)}+\frac{a A c^3 (e x)^{m+1}}{e (m+1)}+\frac{b B d^3 (e x)^{m+11}}{e^{11} (m+11)}",1,"Could not integrate","F",-1
18,0,0,121,0.0567258,"\int (e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^3 \, dx","IntegrateAlgebraic[(e*x)^m*(A + B*x^2)*(c + d*x^2)^3,x]","\int (e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^3 \, dx","\frac{c^2 (e x)^{m+3} (3 A d+B c)}{e^3 (m+3)}+\frac{d^2 (e x)^{m+7} (A d+3 B c)}{e^7 (m+7)}+\frac{3 c d (e x)^{m+5} (A d+B c)}{e^5 (m+5)}+\frac{A c^3 (e x)^{m+1}}{e (m+1)}+\frac{B d^3 (e x)^{m+9}}{e^9 (m+9)}",1,"Could not integrate","F",-1
19,0,0,258,0.4268023,"\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^3}{a+b x^2} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2)*(c + d*x^2)^3)/(a + b*x^2),x]","\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^3}{a+b x^2} \, dx","\frac{d (e x)^{m+3} \left(a^2 B d^2-a b d (A d+3 B c)+3 b^2 c (A d+B c)\right)}{b^3 e^3 (m+3)}-\frac{(e x)^{m+1} \left(a^3 B d^3-a^2 b d^2 (A d+3 B c)+3 a b^2 c d (A d+B c)+b^3 \left(-c^2\right) (3 A d+B c)\right)}{b^4 e (m+1)}+\frac{(e x)^{m+1} (A b-a B) (b c-a d)^3 \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b^4 e (m+1)}+\frac{d^2 (e x)^{m+5} (-a B d+A b d+3 b B c)}{b^2 e^5 (m+5)}+\frac{B d^3 (e x)^{m+7}}{b e^7 (m+7)}",1,"Could not integrate","F",-1
20,0,0,347,0.7191479,"\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^3}{\left(a+b x^2\right)^2} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2)*(c + d*x^2)^3)/(a + b*x^2)^2,x]","\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^3}{\left(a+b x^2\right)^2} \, dx","\frac{(e x)^{m+1} (b c-a d)^2 \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right) (A b (a d (m+5)+b (c-c m))+a B (b c (m+1)-a d (m+7)))}{2 a^2 b^4 e (m+1)}-\frac{d (e x)^{m+1} \left(A b \left(a^2 d^2 (m+5)-3 a b c d (m+3)+3 b^2 c^2 (m+1)\right)-a B \left(a^2 d^2 (m+7)-3 a b c d (m+5)+3 b^2 c^2 (m+3)\right)\right)}{2 a b^4 e (m+1)}-\frac{d^2 (e x)^{m+3} (A b (3 b c (m+3)-a d (m+5))-a B (3 b c (m+5)-a d (m+7)))}{2 a b^3 e^3 (m+3)}-\frac{d^3 (e x)^{m+5} (A b (m+5)-a B (m+7))}{2 a b^2 e^5 (m+5)}+\frac{\left(c+d x^2\right)^3 (e x)^{m+1} (A b-a B)}{2 a b e \left(a+b x^2\right)}",1,"Could not integrate","F",-1
21,0,0,480,0.6041206,"\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^3}{\left(a+b x^2\right)^3} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2)*(c + d*x^2)^3)/(a + b*x^2)^3,x]","\int \frac{(e x)^m \left(A+B x^2\right) \left(c+d x^2\right)^3}{\left(a+b x^2\right)^3} \, dx","-\frac{d^2 (e x)^{m+3} \left(A b (m+3) (a d (m+5)+b c (3-m))+a B \left(b c \left(m^2+4 m+3\right)-a d \left(m^2+12 m+35\right)\right)\right)}{8 a^2 b^3 e^3 (m+3)}+\frac{\left(c+d x^2\right)^2 (e x)^{m+1} (A b (a d (m+3)+b c (3-m))+a B (b c (m+1)-a d (m+7)))}{8 a^2 b^2 e \left(a+b x^2\right)}-\frac{d (e x)^{m+1} \left(A b \left(-a^2 d^2 \left(m^2+8 m+15\right)+3 a b c d \left(m^2+4 m+3\right)+2 b^2 c^2 \left(-m^2+2 m+3\right)\right)+a B \left(a^2 d^2 \left(m^2+12 m+35\right)-3 a b c d \left(m^2+8 m+15\right)+2 b^2 c^2 (m+1)^2\right)\right)}{8 a^2 b^4 e (m+1)}+\frac{(e x)^{m+1} (b c-a d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right) \left(A b \left(a^2 d^2 \left(m^2+8 m+15\right)+2 a b c d \left(-m^2-2 m+3\right)+b^2 c^2 \left(m^2-4 m+3\right)\right)+a B \left(-a^2 d^2 \left(m^2+12 m+35\right)+2 a b c d \left(m^2+6 m+5\right)+b^2 c^2 \left(1-m^2\right)\right)\right)}{8 a^3 b^4 e (m+1)}+\frac{\left(c+d x^2\right)^3 (e x)^{m+1} (A b-a B)}{4 a b e \left(a+b x^2\right)^2}",1,"Could not integrate","F",-1
22,0,0,363,0.3766517,"\int \frac{(e x)^m \left(a+b x^2\right)^4 \left(A+B x^2\right)}{c+d x^2} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x^2)^4*(A + B*x^2))/(c + d*x^2),x]","\int \frac{(e x)^m \left(a+b x^2\right)^4 \left(A+B x^2\right)}{c+d x^2} \, dx","\frac{b^2 (e x)^{m+5} \left(6 a^2 B d^2-4 a b d (B c-A d)+b^2 c (B c-A d)\right)}{d^3 e^5 (m+5)}+\frac{b (e x)^{m+3} \left(4 a^3 B d^3-6 a^2 b d^2 (B c-A d)+4 a b^2 c d (B c-A d)+b^3 \left(-c^2\right) (B c-A d)\right)}{d^4 e^3 (m+3)}+\frac{(e x)^{m+1} \left(a^4 B d^4-4 a^3 b d^3 (B c-A d)+6 a^2 b^2 c d^2 (B c-A d)-4 a b^3 c^2 d (B c-A d)+b^4 c^3 (B c-A d)\right)}{d^5 e (m+1)}-\frac{b^3 (e x)^{m+7} (-4 a B d-A b d+b B c)}{d^2 e^7 (m+7)}-\frac{(e x)^{m+1} (b c-a d)^4 (B c-A d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c d^5 e (m+1)}+\frac{b^4 B (e x)^{m+9}}{d e^9 (m+9)}",1,"Could not integrate","F",-1
23,0,0,260,0.3501111,"\int \frac{(e x)^m \left(a+b x^2\right)^3 \left(A+B x^2\right)}{c+d x^2} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x^2)^3*(A + B*x^2))/(c + d*x^2),x]","\int \frac{(e x)^m \left(a+b x^2\right)^3 \left(A+B x^2\right)}{c+d x^2} \, dx","\frac{b (e x)^{m+3} \left(3 a^2 B d^2-3 a b d (B c-A d)+b^2 c (B c-A d)\right)}{d^3 e^3 (m+3)}+\frac{(e x)^{m+1} \left(a^3 B d^3-3 a^2 b d^2 (B c-A d)+3 a b^2 c d (B c-A d)+b^3 \left(-c^2\right) (B c-A d)\right)}{d^4 e (m+1)}-\frac{b^2 (e x)^{m+5} (-3 a B d-A b d+b B c)}{d^2 e^5 (m+5)}+\frac{(e x)^{m+1} (b c-a d)^3 (B c-A d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c d^4 e (m+1)}+\frac{b^3 B (e x)^{m+7}}{d e^7 (m+7)}",1,"Could not integrate","F",-1
24,0,0,180,0.1256239,"\int \frac{(e x)^m \left(a+b x^2\right)^2 \left(A+B x^2\right)}{c+d x^2} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x^2)^2*(A + B*x^2))/(c + d*x^2),x]","\int \frac{(e x)^m \left(a+b x^2\right)^2 \left(A+B x^2\right)}{c+d x^2} \, dx","\frac{(e x)^{m+1} \left(a^2 B d^2-2 a b d (B c-A d)+b^2 c (B c-A d)\right)}{d^3 e (m+1)}-\frac{(e x)^{m+1} (b c-a d)^2 (B c-A d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c d^3 e (m+1)}-\frac{b (e x)^{m+3} (-2 a B d-A b d+b B c)}{d^2 e^3 (m+3)}+\frac{b^2 B (e x)^{m+5}}{d e^5 (m+5)}",1,"Could not integrate","F",-1
25,0,0,120,0.219918,"\int \frac{(e x)^m \left(a+b x^2\right) \left(A+B x^2\right)}{c+d x^2} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x^2)*(A + B*x^2))/(c + d*x^2),x]","\int \frac{(e x)^m \left(a+b x^2\right) \left(A+B x^2\right)}{c+d x^2} \, dx","\frac{(e x)^{m+1} (b c-a d) (B c-A d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c d^2 e (m+1)}-\frac{(e x)^{m+1} (-a B d-A b d+b B c)}{d^2 e (m+1)}+\frac{b B (e x)^{m+3}}{d e^3 (m+3)}",1,"Could not integrate","F",-1
26,0,0,77,0.0252863,"\int \frac{(e x)^m \left(A+B x^2\right)}{c+d x^2} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2))/(c + d*x^2),x]","\int \frac{(e x)^m \left(A+B x^2\right)}{c+d x^2} \, dx","\frac{B (e x)^{m+1}}{d e (m+1)}-\frac{(e x)^{m+1} (B c-A d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c d e (m+1)}",1,"Could not integrate","F",-1
27,0,0,125,0.2213976,"\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2))/((a + b*x^2)*(c + d*x^2)),x]","\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","\frac{(e x)^{m+1} (A b-a B) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a e (m+1) (b c-a d)}+\frac{(e x)^{m+1} (B c-A d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c e (m+1) (b c-a d)}",1,"Could not integrate","F",-1
28,0,0,206,0.573929,"\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2))/((a + b*x^2)^2*(c + d*x^2)),x]","\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right) (A b (b c (1-m)-a d (3-m))+a B (a d (1-m)+b c (m+1)))}{2 a^2 e (m+1) (b c-a d)^2}-\frac{d (e x)^{m+1} (B c-A d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c e (m+1) (b c-a d)^2}+\frac{(e x)^{m+1} (A b-a B)}{2 a e \left(a+b x^2\right) (b c-a d)}",1,"Could not integrate","F",-1
29,0,0,342,0.9453875,"\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right)^3 \left(c+d x^2\right)} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2))/((a + b*x^2)^3*(c + d*x^2)),x]","\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right)^3 \left(c+d x^2\right)} \, dx","\frac{(e x)^{m+1} (A b (b c (3-m)-a d (7-m))+a B (a d (3-m)+b c (m+1)))}{8 a^2 e \left(a+b x^2\right) (b c-a d)^2}+\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right) \left(A b \left(a^2 d^2 \left(m^2-8 m+15\right)-2 a b c d \left(m^2-6 m+5\right)+b^2 c^2 \left(m^2-4 m+3\right)\right)+a B \left(-a^2 d^2 \left(m^2-4 m+3\right)-2 a b c d \left(-m^2+2 m+3\right)+b^2 c^2 \left(1-m^2\right)\right)\right)}{8 a^3 e (m+1) (b c-a d)^3}+\frac{d^2 (e x)^{m+1} (B c-A d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c e (m+1) (b c-a d)^3}+\frac{(e x)^{m+1} (A b-a B)}{4 a e \left(a+b x^2\right)^2 (b c-a d)}",1,"Could not integrate","F",-1
30,0,0,340,0.5809653,"\int \frac{(e x)^m \left(a+b x^2\right)^3 \left(A+B x^2\right)}{\left(c+d x^2\right)^2} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x^2)^3*(A + B*x^2))/(c + d*x^2)^2,x]","\int \frac{(e x)^m \left(a+b x^2\right)^3 \left(A+B x^2\right)}{\left(c+d x^2\right)^2} \, dx","-\frac{b (e x)^{m+1} \left(3 a^2 d^2 (A d (m+1)-B c (m+3))-3 a b c d (A d (m+3)-B c (m+5))+b^2 c^2 (A d (m+5)-B c (m+7))\right)}{2 c d^4 e (m+1)}-\frac{b^2 (e x)^{m+3} (3 a d (A d (m+3)-B c (m+5))-b c (A d (m+5)-B c (m+7)))}{2 c d^3 e^3 (m+3)}+\frac{(e x)^{m+1} (b c-a d)^2 \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right) (a d (A d (1-m)+B c (m+1))+b c (A d (m+5)-B c (m+7)))}{2 c^2 d^4 e (m+1)}-\frac{\left(a+b x^2\right)^3 (e x)^{m+1} (B c-A d)}{2 c d e \left(c+d x^2\right)}-\frac{b^3 (e x)^{m+5} (A d (m+5)-B c (m+7))}{2 c d^2 e^5 (m+5)}",1,"Could not integrate","F",-1
31,0,0,246,0.565912,"\int \frac{(e x)^m \left(a+b x^2\right)^2 \left(A+B x^2\right)}{\left(c+d x^2\right)^2} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x^2)^2*(A + B*x^2))/(c + d*x^2)^2,x]","\int \frac{(e x)^m \left(a+b x^2\right)^2 \left(A+B x^2\right)}{\left(c+d x^2\right)^2} \, dx","-\frac{(e x)^{m+1} (b c-a d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right) (a d (A d (1-m)+B c (m+1))+b c (A d (m+3)-B c (m+5)))}{2 c^2 d^3 e (m+1)}-\frac{b (e x)^{m+1} (2 a d (A d (m+1)-B c (m+3))-b c (A d (m+3)-B c (m+5)))}{2 c d^3 e (m+1)}-\frac{\left(a+b x^2\right)^2 (e x)^{m+1} (B c-A d)}{2 c d e \left(c+d x^2\right)}-\frac{b^2 (e x)^{m+3} (A d (m+3)-B c (m+5))}{2 c d^2 e^3 (m+3)}",1,"Could not integrate","F",-1
32,0,0,171,0.2576699,"\int \frac{(e x)^m \left(a+b x^2\right) \left(A+B x^2\right)}{\left(c+d x^2\right)^2} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x^2)*(A + B*x^2))/(c + d*x^2)^2,x]","\int \frac{(e x)^m \left(a+b x^2\right) \left(A+B x^2\right)}{\left(c+d x^2\right)^2} \, dx","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right) (a d (A d (1-m)+B c (m+1))+b c (A d (m+1)-B c (m+3)))}{2 c^2 d^2 e (m+1)}-\frac{\left(A+B x^2\right) (e x)^{m+1} (b c-a d)}{2 c d e \left(c+d x^2\right)}-\frac{B (e x)^{m+1} (a d (m+1)-b c (m+3))}{2 c d^2 e (m+1)}",1,"Could not integrate","F",-1
33,0,0,103,0.0359032,"\int \frac{(e x)^m \left(A+B x^2\right)}{\left(c+d x^2\right)^2} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2))/(c + d*x^2)^2,x]","\int \frac{(e x)^m \left(A+B x^2\right)}{\left(c+d x^2\right)^2} \, dx","\frac{(e x)^{m+1} (A d (1-m)+B c (m+1)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{2 c^2 d e (m+1)}-\frac{(e x)^{m+1} (B c-A d)}{2 c d e \left(c+d x^2\right)}",1,"Could not integrate","F",-1
34,0,0,205,0.4069452,"\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2))/((a + b*x^2)*(c + d*x^2)^2),x]","\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right) (a d (A d (1-m)+B c (m+1))+b c (B c (1-m)-A d (3-m)))}{2 c^2 e (m+1) (b c-a d)^2}+\frac{b (e x)^{m+1} (A b-a B) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a e (m+1) (b c-a d)^2}+\frac{(e x)^{m+1} (B c-A d)}{2 c e \left(c+d x^2\right) (b c-a d)}",1,"Could not integrate","F",-1
35,0,0,304,0.9706943,"\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2))/((a + b*x^2)^2*(c + d*x^2)^2),x]","\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","\frac{b (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right) (A b (b c (1-m)-a d (5-m))+a B (a d (3-m)+b c (m+1)))}{2 a^2 e (m+1) (b c-a d)^3}-\frac{d (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right) (a d (A d (1-m)+B c (m+1))+b c (B c (3-m)-A d (5-m)))}{2 c^2 e (m+1) (b c-a d)^3}+\frac{d (e x)^{m+1} (a A d-2 a B c+A b c)}{2 a c e \left(c+d x^2\right) (b c-a d)^2}+\frac{(e x)^{m+1} (A b-a B)}{2 a e \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}",1,"Could not integrate","F",-1
36,0,0,491,1.0299942,"\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right)^3 \left(c+d x^2\right)^2} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2))/((a + b*x^2)^3*(c + d*x^2)^2),x]","\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right)^3 \left(c+d x^2\right)^2} \, dx","-\frac{d (e x)^{m+1} \left(A \left(4 a^2 d^2+a b c d (11-m)-b^2 c^2 (3-m)\right)-a B c (a d (11-m)+b c (m+1))\right)}{8 a^2 c e \left(c+d x^2\right) (b c-a d)^3}+\frac{(e x)^{m+1} (A b (b c (3-m)-a d (9-m))+a B (a d (5-m)+b c (m+1)))}{8 a^2 e \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)^2}+\frac{b (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right) \left(A b \left(a^2 d^2 \left(m^2-12 m+35\right)-2 a b c d \left(m^2-8 m+7\right)+b^2 c^2 \left(m^2-4 m+3\right)\right)+a B \left(-a^2 d^2 \left(m^2-8 m+15\right)-2 a b c d \left(-m^2+4 m+5\right)+b^2 c^2 \left(1-m^2\right)\right)\right)}{8 a^3 e (m+1) (b c-a d)^4}+\frac{d^2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right) (a d (A d (1-m)+B c (m+1))+b c (B c (5-m)-A d (7-m)))}{2 c^2 e (m+1) (b c-a d)^4}+\frac{(e x)^{m+1} (A b-a B)}{4 a e \left(a+b x^2\right)^2 \left(c+d x^2\right) (b c-a d)}",1,"Could not integrate","F",-1
37,0,0,433,0.5997037,"\int \frac{(e x)^m \left(a+b x^2\right)^3 \left(A+B x^2\right)}{\left(c+d x^2\right)^3} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x^2)^3*(A + B*x^2))/(c + d*x^2)^3,x]","\int \frac{(e x)^m \left(a+b x^2\right)^3 \left(A+B x^2\right)}{\left(c+d x^2\right)^3} \, dx","-\frac{b (e x)^{m+1} \left(2 a^2 d^2 (m+1) (A d (3-m)+B c (m+1))+3 a b c d (m+3) (A d (m+1)-B c (m+5))-b^2 c^2 (m+5) (A d (m+3)-B c (m+7))\right)}{8 c^2 d^4 e (m+1)}-\frac{(e x)^{m+1} (b c-a d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right) \left(a^2 d^2 (1-m) (A d (3-m)+B c (m+1))+2 a b c d \left(A d \left(-m^2-2 m+3\right)+B c \left(m^2+6 m+5\right)\right)+b^2 c^2 (m+5) (A d (m+3)-B c (m+7))\right)}{8 c^3 d^4 e (m+1)}-\frac{b^2 (e x)^{m+3} (a d (m+3) (A d (3-m)+B c (m+1))+b c (m+5) (A d (m+3)-B c (m+7)))}{8 c^2 d^3 e^3 (m+3)}+\frac{\left(a+b x^2\right)^2 (e x)^{m+1} (a d (A d (3-m)+B c (m+1))+b c (A d (m+3)-B c (m+7)))}{8 c^2 d^2 e \left(c+d x^2\right)}-\frac{\left(a+b x^2\right)^3 (e x)^{m+1} (B c-A d)}{4 c d e \left(c+d x^2\right)^2}",1,"Could not integrate","F",-1
38,0,0,292,0.7733365,"\int \frac{(e x)^m \left(a+b x^2\right)^2 \left(A+B x^2\right)}{\left(c+d x^2\right)^3} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x^2)^2*(A + B*x^2))/(c + d*x^2)^3,x]","\int \frac{(e x)^m \left(a+b x^2\right)^2 \left(A+B x^2\right)}{\left(c+d x^2\right)^3} \, dx","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right) (a d (a d (1-m)+b c (m+1)) (A d (3-m)+B c (m+1))-b c (a d (m+1)-b c (m+3)) (A d (m+1)-B c (m+5)))}{8 c^3 d^3 e (m+1)}+\frac{b (e x)^{m+1} (a d (m+1)-b c (m+3)) (A d (m+1)-B c (m+5))}{8 c^2 d^3 e (m+1)}-\frac{(e x)^{m+1} (b c-a d) \left(a (A d (3-m)+B c (m+1))-b x^2 (A d (m+1)-B c (m+5))\right)}{8 c^2 d^2 e \left(c+d x^2\right)}-\frac{\left(a+b x^2\right)^2 (e x)^{m+1} (B c-A d)}{4 c d e \left(c+d x^2\right)^2}",1,"Could not integrate","F",-1
39,0,0,208,0.3396752,"\int \frac{(e x)^m \left(a+b x^2\right) \left(A+B x^2\right)}{\left(c+d x^2\right)^3} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x^2)*(A + B*x^2))/(c + d*x^2)^3,x]","\int \frac{(e x)^m \left(a+b x^2\right) \left(A+B x^2\right)}{\left(c+d x^2\right)^3} \, dx","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right) (a d (1-m) (A d (3-m)+B c (m+1))+b c (m+1) (A d (1-m)+B c (m+3)))}{8 c^3 d^2 e (m+1)}+\frac{(e x)^{m+1} (a d (A d (3-m)-B (c-c m))+b c (A d (m+1)-B c (m+3)))}{8 c^2 d^2 e \left(c+d x^2\right)}-\frac{\left(A+B x^2\right) (e x)^{m+1} (b c-a d)}{4 c d e \left(c+d x^2\right)^2}",1,"Could not integrate","F",-1
40,0,0,103,0.0518657,"\int \frac{(e x)^m \left(A+B x^2\right)}{\left(c+d x^2\right)^3} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2))/(c + d*x^2)^3,x]","\int \frac{(e x)^m \left(A+B x^2\right)}{\left(c+d x^2\right)^3} \, dx","\frac{(e x)^{m+1} (A d (3-m)+B c (m+1)) \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{4 c^3 d e (m+1)}-\frac{(e x)^{m+1} (B c-A d)}{4 c d e \left(c+d x^2\right)^2}",1,"Could not integrate","F",-1
41,0,0,333,0.799483,"\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2))/((a + b*x^2)*(c + d*x^2)^3),x]","\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","\frac{(e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right) \left(-a^2 d^2 (1-m) (A d (3-m)+B c (m+1))+2 a b c d \left(A d \left(m^2-6 m+5\right)+B c \left(-m^2+2 m+3\right)\right)+b^2 c^2 (3-m) (B c (1-m)-A d (5-m))\right)}{8 c^3 e (m+1) (b c-a d)^3}+\frac{b^2 (e x)^{m+1} (A b-a B) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a e (m+1) (b c-a d)^3}+\frac{(e x)^{m+1} (a d (A d (3-m)+B c (m+1))+b c (B c (3-m)-A d (7-m)))}{8 c^2 e \left(c+d x^2\right) (b c-a d)^2}+\frac{(e x)^{m+1} (B c-A d)}{4 c e \left(c+d x^2\right)^2 (b c-a d)}",1,"Could not integrate","F",-1
42,0,0,452,1.0633626,"\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2))/((a + b*x^2)^2*(c + d*x^2)^3),x]","\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","\frac{d (e x)^{m+1} \left(A \left(-a^2 d^2 (3-m)+a b c d (11-m)+4 b^2 c^2\right)-a B c (a d (m+1)+b c (11-m))\right)}{8 a c^2 e \left(c+d x^2\right) (b c-a d)^3}-\frac{d (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right) \left(-a^2 d^2 (1-m) (A d (3-m)+B c (m+1))+2 a b c d \left(A d \left(m^2-8 m+7\right)+B c \left(-m^2+4 m+5\right)\right)+b^2 c^2 (5-m) (B c (3-m)-A d (7-m))\right)}{8 c^3 e (m+1) (b c-a d)^4}+\frac{b^2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right) (A b (b c (1-m)-a d (7-m))+a B (a d (5-m)+b c (m+1)))}{2 a^2 e (m+1) (b c-a d)^4}+\frac{d (e x)^{m+1} (a A d-3 a B c+2 A b c)}{4 a c e \left(c+d x^2\right)^2 (b c-a d)^2}+\frac{(e x)^{m+1} (A b-a B)}{2 a e \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}",1,"Could not integrate","F",-1
43,0,0,665,1.1836821,"\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right)^3 \left(c+d x^2\right)^3} \, dx","IntegrateAlgebraic[((e*x)^m*(A + B*x^2))/((a + b*x^2)^3*(c + d*x^2)^3),x]","\int \frac{(e x)^m \left(A+B x^2\right)}{\left(a+b x^2\right)^3 \left(c+d x^2\right)^3} \, dx","\frac{d (e x)^{m+1} \left(A (a d+b c) \left(a^2 d^2 (3-m)-2 a b c d (9-m)+b^2 c^2 (3-m)\right)+a B c \left(a^2 d^2 (m+1)+2 a b c d (11-m)+b^2 c^2 (m+1)\right)\right)}{8 a^2 c^2 e \left(c+d x^2\right) (b c-a d)^4}-\frac{d (e x)^{m+1} \left(A \left(2 a^2 d^2+a b c d (13-m)-b^2 c^2 (3-m)\right)-a B c (a d (11-m)+b c (m+1))\right)}{8 a^2 c e \left(c+d x^2\right)^2 (b c-a d)^3}+\frac{d^2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right) \left(-a^2 d^2 (1-m) (A d (3-m)+B c (m+1))+2 a b c d \left(A d \left(m^2-10 m+9\right)+B c \left(-m^2+6 m+7\right)\right)+b^2 c^2 (7-m) (B c (5-m)-A d (9-m))\right)}{8 c^3 e (m+1) (b c-a d)^5}+\frac{(e x)^{m+1} (A b (b c (3-m)-a d (11-m))+a B (a d (7-m)+b c (m+1)))}{8 a^2 e \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)^2}+\frac{b^2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right) \left(A b \left(a^2 d^2 \left(m^2-16 m+63\right)-2 a b c d \left(m^2-10 m+9\right)+b^2 c^2 \left(m^2-4 m+3\right)\right)+a B \left(-a^2 d^2 \left(m^2-12 m+35\right)-2 a b c d \left(-m^2+6 m+7\right)+b^2 c^2 \left(1-m^2\right)\right)\right)}{8 a^3 e (m+1) (b c-a d)^5}+\frac{(e x)^{m+1} (A b-a B)}{4 a e \left(a+b x^2\right)^2 \left(c+d x^2\right)^2 (b c-a d)}",1,"Could not integrate","F",-1
44,0,0,1059,0.0659362,"\int (e x)^m \left(a+b x^2\right)^p \left(A+B x^2\right) \left(c+d x^2\right)^3 \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x^2)^p*(A + B*x^2)*(c + d*x^2)^3,x]","\int (e x)^m \left(a+b x^2\right)^p \left(A+B x^2\right) \left(c+d x^2\right)^3 \, dx","-\frac{\left(-c^2 \left(48 B c+A d \left(m^3+(6 p+23) m^2+\left(12 p^2+92 p+183\right) m+8 p^3+92 p^2+366 p+513\right)\right) b^3+a c d \left(2 A d \left(m^3+4 (p+5) m^2+\left(4 p^2+44 p+123\right) m+8 p^2+84 p+216\right)+B c \left(m^3+(4 p+21) m^2+\left(4 p^2+44 p+143\right) m+4 p^2+40 p+267\right)\right) b^2-a^2 d^2 (m+5) \left(A d (m+3) (m+2 p+9)+2 B c \left(m^2+2 p m+13 m+2 p+30\right)\right) b+a^3 B d^3 \left(m^3+15 m^2+71 m+105\right)\right) \left(b x^2+a\right)^{p+1} (e x)^{m+1}}{b^4 e (m+2 p+3) (m+2 p+5) (m+2 p+7) (m+2 p+9)}+\frac{B \left(b x^2+a\right)^{p+1} \left(d x^2+c\right)^3 (e x)^{m+1}}{b e (m+2 p+9)}-\frac{(a B d (m+7)-b (6 B c+A d (m+2 p+9))) \left(b x^2+a\right)^{p+1} \left(d x^2+c\right)^2 (e x)^{m+1}}{b^2 e (m+2 p+7) (m+2 p+9)}+\frac{\left(c \left(24 B c+A d \left(m^2+4 (p+5) m+4 p^2+40 p+99\right)\right) b^2-a d \left(A d (m+5) (m+2 p+9)+B c \left(m^2+2 (p+9) m+2 p+65\right)\right) b+a^2 B d^2 \left(m^2+12 m+35\right)\right) \left(b x^2+a\right)^{p+1} \left(d x^2+c\right) (e x)^{m+1}}{b^3 e (m+2 p+5) (m+2 p+7) (m+2 p+9)}+\frac{\left(a (m+1) \left(-c^2 \left(48 B c+A d \left(m^3+(6 p+23) m^2+\left(12 p^2+92 p+183\right) m+8 p^3+92 p^2+366 p+513\right)\right) b^3+a c d \left(2 A d \left(m^3+4 (p+5) m^2+\left(4 p^2+44 p+123\right) m+8 p^2+84 p+216\right)+B c \left(m^3+(4 p+21) m^2+\left(4 p^2+44 p+143\right) m+4 p^2+40 p+267\right)\right) b^2-a^2 d^2 (m+5) \left(A d (m+3) (m+2 p+9)+2 B c \left(m^2+2 p m+13 m+2 p+30\right)\right) b+a^3 B d^3 \left(m^3+15 m^2+71 m+105\right)\right)-b c (m+2 p+3) (2 b c (p+2) (2 b c (p+3) (a B (m+1)-A b (m+2 p+9))+(b c-a d) (m+1) (a B (m+7)-A b (m+2 p+9)))+(m+1) (b c (2 b c (p+3) (a B (m+1)-A b (m+2 p+9))+(b c-a d) (m+1) (a B (m+7)-A b (m+2 p+9)))-a (2 b c d (p+3) (a B (m+1)-A b (m+2 p+9))+d (b c-a d) (m+1) (a B (m+7)-A b (m+2 p+9))+4 (b c-a d) (a B d (m+7)-b (6 B c+A d (m+2 p+9))))))\right) \left(b x^2+a\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{b x^2}{a}\right) (e x)^{m+1}}{b^4 e (m+1) (m+2 p+3) (m+2 p+5) (m+2 p+7) (m+2 p+9)}",1,"Could not integrate","F",-1
45,0,0,495,0.0415595,"\int (e x)^m \left(a+b x^2\right)^p \left(A+B x^2\right) \left(c+d x^2\right)^2 \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x^2)^p*(A + B*x^2)*(c + d*x^2)^2,x]","\int (e x)^m \left(a+b x^2\right)^p \left(A+B x^2\right) \left(c+d x^2\right)^2 \, dx","\frac{(e x)^{m+1} \left(a+b x^2\right)^{p+1} \left(a^2 B d^2 \left(m^2+8 m+15\right)-a b d \left(A d (m+3) (m+2 p+7)+B c \left(m^2+2 m (p+6)+2 p+27\right)\right)+b^2 c \left(A d (m+2 p+7)^2+8 B c\right)\right)}{b^3 e (m+2 p+3) (m+2 p+5) (m+2 p+7)}-\frac{(e x)^{m+1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{b x^2}{a}\right) (b c (m+2 p+3) ((m+1) (b c-a d) (a B (m+5)-A b (m+2 p+7))+2 b c (p+2) (a B (m+1)-A b (m+2 p+7)))-a (m+1) (2 b c d (p+2) (a B (m+1)-A b (m+2 p+7))+d (m+1) (b c-a d) (a B (m+5)-A b (m+2 p+7))+2 (b c-a d) (a B d (m+5)-b (A d (m+2 p+7)+4 B c))))}{b^3 e (m+1) (m+2 p+3) (m+2 p+5) (m+2 p+7)}-\frac{\left(c+d x^2\right) (e x)^{m+1} \left(a+b x^2\right)^{p+1} (a B d (m+5)-b (A d (m+2 p+7)+4 B c))}{b^2 e (m+2 p+5) (m+2 p+7)}+\frac{B \left(c+d x^2\right)^2 (e x)^{m+1} \left(a+b x^2\right)^{p+1}}{b e (m+2 p+7)}",1,"Could not integrate","F",-1
46,0,0,253,0.0307529,"\int (e x)^m \left(a+b x^2\right)^p \left(A+B x^2\right) \left(c+d x^2\right) \, dx","IntegrateAlgebraic[(e*x)^m*(a + b*x^2)^p*(A + B*x^2)*(c + d*x^2),x]","\int (e x)^m \left(a+b x^2\right)^p \left(A+B x^2\right) \left(c+d x^2\right) \, dx","-\frac{(e x)^{m+1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{b x^2}{a}\right) (A b (m+2 p+3) (a d (m+1)-b c (m+2 p+5))-a (m+1) (a B d (m+3)-b (2 A d+B c (m+2 p+5))))}{b^2 e (m+1) (m+2 p+3) (m+2 p+5)}-\frac{(e x)^{m+1} \left(a+b x^2\right)^{p+1} (a B d (m+3)-b (2 A d+B c (m+2 p+5)))}{b^2 e (m+2 p+3) (m+2 p+5)}+\frac{d \left(A+B x^2\right) (e x)^{m+1} \left(a+b x^2\right)^{p+1}}{b e (m+2 p+5)}",1,"Could not integrate","F",-1
47,0,0,162,0.041811,"\int \frac{(e x)^m \left(a+b x^2\right)^p \left(A+B x^2\right)}{c+d x^2} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x^2)^p*(A + B*x^2))/(c + d*x^2),x]","\int \frac{(e x)^m \left(a+b x^2\right)^p \left(A+B x^2\right)}{c+d x^2} \, dx","\frac{B (e x)^{m+1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{b x^2}{a}\right)}{d e (m+1)}-\frac{(e x)^{m+1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} (B c-A d) F_1\left(\frac{m+1}{2};-p,1;\frac{m+3}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{c d e (m+1)}",1,"Could not integrate","F",-1
48,0,0,295,0.0545074,"\int \frac{(e x)^m \left(a+b x^2\right)^p \left(A+B x^2\right)}{\left(c+d x^2\right)^2} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x^2)^p*(A + B*x^2))/(c + d*x^2)^2,x]","\int \frac{(e x)^m \left(a+b x^2\right)^p \left(A+B x^2\right)}{\left(c+d x^2\right)^2} \, dx","-\frac{(e x)^{m+1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} (a d (A d (1-m)+B c (m+1))-b c (A d (-m-2 p+1)+B c (m+2 p+1))) F_1\left(\frac{m+1}{2};-p,1;\frac{m+3}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{2 c^2 d e (m+1) (b c-a d)}-\frac{b (m+2 p+1) (e x)^{m+1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} (B c-A d) \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 c d e (m+1) (b c-a d)}+\frac{(e x)^{m+1} \left(a+b x^2\right)^{p+1} (B c-A d)}{2 c e \left(c+d x^2\right) (b c-a d)}",1,"Could not integrate","F",-1
49,0,0,483,0.0810261,"\int \frac{(e x)^m \left(a+b x^2\right)^p \left(A+B x^2\right)}{\left(c+d x^2\right)^3} \, dx","IntegrateAlgebraic[((e*x)^m*(a + b*x^2)^p*(A + B*x^2))/(c + d*x^2)^3,x]","\int \frac{(e x)^m \left(a+b x^2\right)^p \left(A+B x^2\right)}{\left(c+d x^2\right)^3} \, dx","\frac{(e x)^{m+1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(a^2 d^2 (1-m) (A d (3-m)+B c (m+1))-2 a b c d (A d (1-m) (-m-2 p+3)+B c (m+1) (-m-2 p+1))+b^2 c^2 (-m-2 p+1) (A d (-m-2 p+3)+B c (m+2 p+1))\right) F_1\left(\frac{m+1}{2};-p,1;\frac{m+3}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{8 c^3 d e (m+1) (b c-a d)^2}-\frac{b (m+2 p+1) (e x)^{m+1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{b x^2}{a}\right) (a d (A d (3-m)+B c (m+1))+b c (B c (-m-2 p+1)-A d (-m-2 p+5)))}{8 c^2 d e (m+1) (b c-a d)^2}+\frac{(e x)^{m+1} \left(a+b x^2\right)^{p+1} (a d (A d (3-m)+B c (m+1))+b c (B c (-m-2 p+1)-A d (-m-2 p+5)))}{8 c^2 e \left(c+d x^2\right) (b c-a d)^2}+\frac{(e x)^{m+1} \left(a+b x^2\right)^{p+1} (B c-A d)}{4 c e \left(c+d x^2\right)^2 (b c-a d)}",1,"Could not integrate","F",-1
50,1,111,84,0.164888,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right) \left(c+d x^2\right)}{x} \, dx","IntegrateAlgebraic[(Sqrt[a + b*x^2]*(A + B*x^2)*(c + d*x^2))/x,x]","\frac{\sqrt{a+b x^2} \left(-2 a^2 B d+5 a A b d+5 a b B c+a b B d x^2+15 A b^2 c+5 A b^2 d x^2+5 b^2 B c x^2+3 b^2 B d x^4\right)}{15 b^2}-\sqrt{a} A c \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)","-\frac{\left(a+b x^2\right)^{3/2} \left(2 a B d-5 b (A d+B c)-3 b B d x^2\right)}{15 b^2}+A c \sqrt{a+b x^2}-\sqrt{a} A c \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)",1,"(Sqrt[a + b*x^2]*(15*A*b^2*c + 5*a*b*B*c + 5*a*A*b*d - 2*a^2*B*d + 5*b^2*B*c*x^2 + 5*A*b^2*d*x^2 + a*b*B*d*x^2 + 3*b^2*B*d*x^4))/(15*b^2) - Sqrt[a]*A*c*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",1
51,1,111,84,0.377308,"\int \frac{\left(a+b x^2\right) \left(A+B x^2\right) \sqrt{c+d x^2}}{x} \, dx","IntegrateAlgebraic[((a + b*x^2)*(A + B*x^2)*Sqrt[c + d*x^2])/x,x]","\frac{\sqrt{c+d x^2} \left(15 a A d^2+5 a B c d+5 a B d^2 x^2+5 A b c d+5 A b d^2 x^2-2 b B c^2+b B c d x^2+3 b B d^2 x^4\right)}{15 d^2}-a A \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)","-\frac{\left(c+d x^2\right)^{3/2} \left(-5 d (a B+A b)+2 b B c-3 b B d x^2\right)}{15 d^2}+a A \sqrt{c+d x^2}-a A \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)",1,"(Sqrt[c + d*x^2]*(-2*b*B*c^2 + 5*A*b*c*d + 5*a*B*c*d + 15*a*A*d^2 + b*B*c*d*x^2 + 5*A*b*d^2*x^2 + 5*a*B*d^2*x^2 + 3*b*B*d^2*x^4))/(15*d^2) - a*A*Sqrt[c]*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]]","A",1