1,1,61,60,0.000000," ","int(x^2*(C*x^2+B*x+A)*(c*x^4+b*x^2+a),x)","\frac{C c \,x^{9}}{9}+\frac{B c \,x^{8}}{8}+\frac{B b \,x^{6}}{6}+\frac{\left(A c +b C \right) x^{7}}{7}+\frac{B a \,x^{4}}{4}+\frac{A a \,x^{3}}{3}+\frac{\left(A b +a C \right) x^{5}}{5}"," ",0,"1/3*a*A*x^3+1/4*a*B*x^4+1/5*(A*b+C*a)*x^5+1/6*b*B*x^6+1/7*(A*c+C*b)*x^7+1/8*B*c*x^8+1/9*c*C*x^9","A"
2,1,61,60,0.003000," ","int(x*(C*x^2+B*x+A)*(c*x^4+b*x^2+a),x)","\frac{C c \,x^{8}}{8}+\frac{B c \,x^{7}}{7}+\frac{B b \,x^{5}}{5}+\frac{\left(A c +b C \right) x^{6}}{6}+\frac{B a \,x^{3}}{3}+\frac{A a \,x^{2}}{2}+\frac{\left(A b +a C \right) x^{4}}{4}"," ",0,"1/2*a*A*x^2+1/3*a*B*x^3+1/4*(A*b+C*a)*x^4+1/5*b*B*x^5+1/6*(A*c+C*b)*x^6+1/7*B*c*x^7+1/8*c*C*x^8","A"
3,1,58,57,0.000000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a),x)","\frac{C c \,x^{7}}{7}+\frac{B c \,x^{6}}{6}+\frac{B b \,x^{4}}{4}+\frac{\left(A c +b C \right) x^{5}}{5}+\frac{B a \,x^{2}}{2}+A a x +\frac{\left(A b +a C \right) x^{3}}{3}"," ",0,"a*A*x+1/2*a*B*x^2+1/3*(A*b+C*a)*x^3+1/4*b*B*x^4+1/5*(A*c+C*b)*x^5+1/6*B*c*x^6+1/7*c*C*x^7","A"
4,1,60,55,0.002000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x,x)","\frac{C c \,x^{6}}{6}+\frac{B c \,x^{5}}{5}+\frac{A c \,x^{4}}{4}+\frac{C b \,x^{4}}{4}+\frac{B b \,x^{3}}{3}+\frac{A b \,x^{2}}{2}+\frac{C a \,x^{2}}{2}+A a \ln \left(x \right)+B a x"," ",0,"1/6*c*C*x^6+1/5*B*c*x^5+1/4*A*x^4*c+1/4*C*x^4*b+1/3*b*B*x^3+1/2*A*x^2*b+1/2*C*x^2*a+a*B*x+a*A*ln(x)","A"
5,1,57,55,0.006000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^2,x)","\frac{C c \,x^{5}}{5}+\frac{B c \,x^{4}}{4}+\frac{A c \,x^{3}}{3}+\frac{C b \,x^{3}}{3}+\frac{B b \,x^{2}}{2}+A b x +B a \ln \left(x \right)+C a x -\frac{A a}{x}"," ",0,"1/5*c*C*x^5+1/4*B*c*x^4+1/3*A*x^3*c+1/3*C*x^3*b+1/2*b*B*x^2+A*b*x+a*C*x+a*B*ln(x)-a*A/x","A"
6,1,58,55,0.010000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^3,x)","\frac{C c \,x^{4}}{4}+\frac{B c \,x^{3}}{3}+\frac{A c \,x^{2}}{2}+\frac{C b \,x^{2}}{2}+A b \ln \left(x \right)+B b x +C a \ln \left(x \right)-\frac{B a}{x}-\frac{A a}{2 x^{2}}"," ",0,"1/4*c*C*x^4+1/3*B*c*x^3+1/2*A*x^2*c+1/2*C*x^2*b+b*B*x+A*ln(x)*b+C*ln(x)*a-a*B/x-1/2*a*A/x^2","A"
7,1,57,56,0.007000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^4,x)","\frac{C c \,x^{3}}{3}+\frac{B c \,x^{2}}{2}+A c x +B b \ln \left(x \right)+C b x -\frac{A b}{x}-\frac{C a}{x}-\frac{B a}{2 x^{2}}-\frac{A a}{3 x^{3}}"," ",0,"1/3*c*C*x^3+1/2*B*c*x^2+A*c*x+b*C*x+b*B*ln(x)-1/x*A*b-1/x*a*C-1/3*a*A/x^3-1/2*a*B/x^2","A"
8,1,58,57,0.006000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^5,x)","\frac{C c \,x^{2}}{2}+A c \ln \left(x \right)+B c x +C b \ln \left(x \right)-\frac{B b}{x}-\frac{A b}{2 x^{2}}-\frac{C a}{2 x^{2}}-\frac{B a}{3 x^{3}}-\frac{A a}{4 x^{4}}"," ",0,"1/2*c*C*x^2+B*c*x+A*ln(x)*c+C*ln(x)*b-b*B/x-1/3*a*B/x^3-1/4*a*A/x^4-1/2/x^2*A*b-1/2/x^2*a*C","A"
9,1,60,58,0.007000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^6,x)","B c \ln \left(x \right)+C c x -\frac{A c}{x}-\frac{C b}{x}-\frac{B b}{2 x^{2}}-\frac{A b}{3 x^{3}}-\frac{C a}{3 x^{3}}-\frac{B a}{4 x^{4}}-\frac{A a}{5 x^{5}}"," ",0,"c*C*x+B*c*ln(x)-1/x*A*c-1/x*b*C-1/3/x^3*A*b-1/3/x^3*a*C-1/5*a*A/x^5-1/4*a*B/x^4-1/2*b*B/x^2","A"
10,1,63,62,0.006000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)/x^7,x)","C c \ln \left(x \right)-\frac{B c}{x}-\frac{A c}{2 x^{2}}-\frac{C b}{2 x^{2}}-\frac{B b}{3 x^{3}}-\frac{A b}{4 x^{4}}-\frac{C a}{4 x^{4}}-\frac{B a}{5 x^{5}}-\frac{A a}{6 x^{6}}"," ",0,"c*C*ln(x)-B*c/x-1/3*b*B/x^3-1/5*a*B/x^5-1/4/x^4*A*b-1/4/x^4*a*C-1/2/x^2*A*c-1/2/x^2*b*C-1/6*a*A/x^6","A"
11,1,142,137,0.001000," ","int(x^2*(C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2,x)","\frac{C \,c^{2} x^{13}}{13}+\frac{B \,c^{2} x^{12}}{12}+\frac{B b c \,x^{10}}{5}+\frac{\left(A \,c^{2}+2 C b c \right) x^{11}}{11}+\frac{B a b \,x^{6}}{3}+\frac{\left(2 a c +b^{2}\right) B \,x^{8}}{8}+\frac{\left(2 A b c +\left(2 a c +b^{2}\right) C \right) x^{9}}{9}+\frac{B \,a^{2} x^{4}}{4}+\frac{\left(2 C a b +\left(2 a c +b^{2}\right) A \right) x^{7}}{7}+\frac{A \,a^{2} x^{3}}{3}+\frac{\left(2 A a b +C \,a^{2}\right) x^{5}}{5}"," ",0,"1/13*c^2*C*x^13+1/12*B*c^2*x^12+1/11*(A*c^2+2*C*b*c)*x^11+1/5*b*B*c*x^10+1/9*(2*A*b*c+(2*a*c+b^2)*C)*x^9+1/8*B*(2*a*c+b^2)*x^8+1/7*(A*(2*a*c+b^2)+2*a*b*C)*x^7+1/3*a*b*B*x^6+1/5*(2*A*a*b+C*a^2)*x^5+1/4*a^2*B*x^4+1/3*a^2*A*x^3","A"
12,1,142,137,0.001000," ","int(x*(C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2,x)","\frac{C \,c^{2} x^{12}}{12}+\frac{B \,c^{2} x^{11}}{11}+\frac{2 B b c \,x^{9}}{9}+\frac{\left(A \,c^{2}+2 C b c \right) x^{10}}{10}+\frac{2 B a b \,x^{5}}{5}+\frac{\left(2 a c +b^{2}\right) B \,x^{7}}{7}+\frac{\left(2 A b c +\left(2 a c +b^{2}\right) C \right) x^{8}}{8}+\frac{B \,a^{2} x^{3}}{3}+\frac{\left(2 C a b +\left(2 a c +b^{2}\right) A \right) x^{6}}{6}+\frac{A \,a^{2} x^{2}}{2}+\frac{\left(2 A a b +C \,a^{2}\right) x^{4}}{4}"," ",0,"1/12*c^2*C*x^12+1/11*B*c^2*x^11+1/10*(A*c^2+2*C*b*c)*x^10+2/9*b*B*c*x^9+1/8*(2*A*b*c+(2*a*c+b^2)*C)*x^8+1/7*B*(2*a*c+b^2)*x^7+1/6*(2*C*a*b+(2*a*c+b^2)*A)*x^6+2/5*a*b*B*x^5+1/4*(2*A*a*b+C*a^2)*x^4+1/3*a^2*B*x^3+1/2*a^2*A*x^2","A"
13,1,139,134,0.002000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2,x)","\frac{C \,c^{2} x^{11}}{11}+\frac{B \,c^{2} x^{10}}{10}+\frac{B b c \,x^{8}}{4}+\frac{\left(A \,c^{2}+2 C b c \right) x^{9}}{9}+\frac{B a b \,x^{4}}{2}+\frac{\left(2 a c +b^{2}\right) B \,x^{6}}{6}+\frac{\left(2 A b c +\left(2 a c +b^{2}\right) C \right) x^{7}}{7}+\frac{B \,a^{2} x^{2}}{2}+\frac{\left(2 C a b +\left(2 a c +b^{2}\right) A \right) x^{5}}{5}+A \,a^{2} x +\frac{\left(2 A a b +C \,a^{2}\right) x^{3}}{3}"," ",0,"1/11*c^2*C*x^11+1/10*B*c^2*x^10+1/9*(A*c^2+2*C*b*c)*x^9+1/4*b*B*c*x^8+1/7*(2*A*b*c+(2*a*c+b^2)*C)*x^7+1/6*B*(2*a*c+b^2)*x^6+1/5*(2*C*a*b+(2*a*c+b^2)*A)*x^5+1/2*a*b*B*x^4+1/3*(2*A*a*b+C*a^2)*x^3+1/2*a^2*B*x^2+a^2*A*x","A"
14,1,149,132,0.004000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x,x)","\frac{C \,c^{2} x^{10}}{10}+\frac{B \,c^{2} x^{9}}{9}+\frac{A \,c^{2} x^{8}}{8}+\frac{C b c \,x^{8}}{4}+\frac{2 B b c \,x^{7}}{7}+\frac{A b c \,x^{6}}{3}+\frac{C a c \,x^{6}}{3}+\frac{C \,b^{2} x^{6}}{6}+\frac{2 B a c \,x^{5}}{5}+\frac{B \,b^{2} x^{5}}{5}+\frac{A a c \,x^{4}}{2}+\frac{A \,b^{2} x^{4}}{4}+\frac{C a b \,x^{4}}{2}+\frac{2 B a b \,x^{3}}{3}+A a b \,x^{2}+\frac{C \,a^{2} x^{2}}{2}+A \,a^{2} \ln \left(x \right)+B \,a^{2} x"," ",0,"1/10*c^2*C*x^10+1/9*B*c^2*x^9+1/8*A*x^8*c^2+1/4*C*x^8*b*c+2/7*b*B*c*x^7+1/3*A*x^6*b*c+1/3*C*x^6*a*c+1/6*C*x^6*b^2+2/5*B*x^5*a*c+1/5*B*x^5*b^2+1/2*A*x^4*a*c+1/4*A*x^4*b^2+1/2*C*x^4*a*b+2/3*a*b*B*x^3+A*x^2*a*b+1/2*C*x^2*a^2+a^2*B*x+a^2*A*ln(x)","A"
15,1,147,131,0.007000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^2,x)","\frac{C \,c^{2} x^{9}}{9}+\frac{B \,c^{2} x^{8}}{8}+\frac{A \,c^{2} x^{7}}{7}+\frac{2 C b c \,x^{7}}{7}+\frac{B b c \,x^{6}}{3}+\frac{2 A b c \,x^{5}}{5}+\frac{2 C a c \,x^{5}}{5}+\frac{C \,b^{2} x^{5}}{5}+\frac{B a c \,x^{4}}{2}+\frac{B \,b^{2} x^{4}}{4}+\frac{2 A a c \,x^{3}}{3}+\frac{A \,b^{2} x^{3}}{3}+\frac{2 C a b \,x^{3}}{3}+B a b \,x^{2}+2 A a b x +B \,a^{2} \ln \left(x \right)+C \,a^{2} x -\frac{A \,a^{2}}{x}"," ",0,"1/9*c^2*C*x^9+1/8*B*c^2*x^8+1/7*A*x^7*c^2+2/7*C*x^7*b*c+1/3*b*B*c*x^6+2/5*A*x^5*b*c+2/5*C*x^5*a*c+1/5*C*x^5*b^2+1/2*B*x^4*a*c+1/4*B*x^4*b^2+2/3*A*x^3*a*c+1/3*A*x^3*b^2+2/3*C*x^3*a*b+a*b*B*x^2+2*A*a*b*x+C*a^2*x+a^2*B*ln(x)-a^2*A/x","A"
16,1,148,133,0.007000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^3,x)","\frac{C \,c^{2} x^{8}}{8}+\frac{B \,c^{2} x^{7}}{7}+\frac{A \,c^{2} x^{6}}{6}+\frac{C b c \,x^{6}}{3}+\frac{2 B b c \,x^{5}}{5}+\frac{A b c \,x^{4}}{2}+\frac{C a c \,x^{4}}{2}+\frac{C \,b^{2} x^{4}}{4}+\frac{2 B a c \,x^{3}}{3}+\frac{B \,b^{2} x^{3}}{3}+A a c \,x^{2}+\frac{A \,b^{2} x^{2}}{2}+C a b \,x^{2}+2 A a b \ln \left(x \right)+2 B a b x +C \,a^{2} \ln \left(x \right)-\frac{B \,a^{2}}{x}-\frac{A \,a^{2}}{2 x^{2}}"," ",0,"1/8*c^2*C*x^8+1/7*B*c^2*x^7+1/6*A*x^6*c^2+1/3*C*x^6*b*c+2/5*b*B*c*x^5+1/2*A*x^4*b*c+1/2*C*x^4*a*c+1/4*C*x^4*b^2+2/3*B*x^3*a*c+1/3*B*x^3*b^2+A*x^2*a*c+1/2*A*x^2*b^2+C*x^2*a*b+2*a*b*B*x+2*A*ln(x)*a*b+C*ln(x)*a^2-a^2*B/x-1/2*a^2*A/x^2","A"
17,1,146,133,0.009000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^4,x)","\frac{C \,c^{2} x^{7}}{7}+\frac{B \,c^{2} x^{6}}{6}+\frac{A \,c^{2} x^{5}}{5}+\frac{2 C b c \,x^{5}}{5}+\frac{B b c \,x^{4}}{2}+\frac{2 A b c \,x^{3}}{3}+\frac{2 C a c \,x^{3}}{3}+\frac{C \,b^{2} x^{3}}{3}+B a c \,x^{2}+\frac{B \,b^{2} x^{2}}{2}+2 A a c x +A \,b^{2} x +2 B a b \ln \left(x \right)+2 C a b x -\frac{2 A a b}{x}-\frac{C \,a^{2}}{x}-\frac{B \,a^{2}}{2 x^{2}}-\frac{A \,a^{2}}{3 x^{3}}"," ",0,"1/7*c^2*C*x^7+1/6*B*c^2*x^6+1/5*A*x^5*c^2+2/5*C*x^5*b*c+1/2*b*B*c*x^4+2/3*A*x^3*b*c+2/3*C*x^3*a*c+1/3*C*x^3*b^2+B*x^2*a*c+1/2*B*x^2*b^2+2*a*A*c*x+A*b^2*x+2*C*a*b*x+2*a*b*B*ln(x)-2*a/x*A*b-a^2/x*C-1/3*a^2*A/x^3-1/2*a^2*B/x^2","A"
18,1,144,132,0.008000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^5,x)","\frac{C \,c^{2} x^{6}}{6}+\frac{B \,c^{2} x^{5}}{5}+\frac{A \,c^{2} x^{4}}{4}+\frac{C b c \,x^{4}}{2}+\frac{2 B b c \,x^{3}}{3}+A b c \,x^{2}+C a c \,x^{2}+\frac{C \,b^{2} x^{2}}{2}+2 A a c \ln \left(x \right)+A \,b^{2} \ln \left(x \right)+2 B a c x +B \,b^{2} x +2 C a b \ln \left(x \right)-\frac{2 B a b}{x}-\frac{A a b}{x^{2}}-\frac{C \,a^{2}}{2 x^{2}}-\frac{B \,a^{2}}{3 x^{3}}-\frac{A \,a^{2}}{4 x^{4}}"," ",0,"1/6*c^2*C*x^6+1/5*B*c^2*x^5+1/4*A*x^4*c^2+1/2*C*x^4*b*c+2/3*b*B*c*x^3+A*x^2*b*c+C*x^2*a*c+1/2*C*x^2*b^2+2*a*B*c*x+b^2*B*x+2*A*ln(x)*a*c+A*ln(x)*b^2+2*C*ln(x)*a*b-2*a*b*B/x-1/3*a^2*B/x^3-1/4*a^2*A/x^4-a/x^2*A*b-1/2*a^2/x^2*C","A"
19,1,144,131,0.009000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^6,x)","\frac{C \,c^{2} x^{5}}{5}+\frac{B \,c^{2} x^{4}}{4}+\frac{A \,c^{2} x^{3}}{3}+\frac{2 C b c \,x^{3}}{3}+B b c \,x^{2}+2 A b c x +2 B a c \ln \left(x \right)+B \,b^{2} \ln \left(x \right)+2 C a c x +C \,b^{2} x -\frac{2 A a c}{x}-\frac{A \,b^{2}}{x}-\frac{2 C a b}{x}-\frac{B a b}{x^{2}}-\frac{2 A a b}{3 x^{3}}-\frac{C \,a^{2}}{3 x^{3}}-\frac{B \,a^{2}}{4 x^{4}}-\frac{A \,a^{2}}{5 x^{5}}"," ",0,"1/5*c^2*C*x^5+1/4*B*c^2*x^4+1/3*A*x^3*c^2+2/3*C*x^3*b*c+b*B*c*x^2+2*A*b*c*x+2*a*c*C*x+b^2*C*x+2*B*ln(x)*a*c+B*ln(x)*b^2-2/x*a*A*c-1/x*A*b^2-2/x*C*a*b-2/3*a/x^3*A*b-1/3*a^2/x^3*C-1/5*a^2*A/x^5-1/4*a^2*B/x^4-a*b*B/x^2","A"
20,1,148,134,0.009000," ","int((C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2/x^7,x)","\frac{C \,c^{2} x^{4}}{4}+\frac{B \,c^{2} x^{3}}{3}+\frac{A \,c^{2} x^{2}}{2}+C b c \,x^{2}+2 A b c \ln \left(x \right)+2 B b c x +2 C a c \ln \left(x \right)+C \,b^{2} \ln \left(x \right)-\frac{2 B a c}{x}-\frac{B \,b^{2}}{x}-\frac{A a c}{x^{2}}-\frac{A \,b^{2}}{2 x^{2}}-\frac{C a b}{x^{2}}-\frac{2 B a b}{3 x^{3}}-\frac{A a b}{2 x^{4}}-\frac{C \,a^{2}}{4 x^{4}}-\frac{B \,a^{2}}{5 x^{5}}-\frac{A \,a^{2}}{6 x^{6}}"," ",0,"1/4*c^2*C*x^4+1/3*B*c^2*x^3+1/2*A*x^2*c^2+C*x^2*b*c+2*b*B*c*x+2*A*ln(x)*b*c+2*C*ln(x)*a*c+C*ln(x)*b^2-2*B/x*a*c-B/x*b^2-2/3*a*b*B/x^3-1/5*a^2*B/x^5-1/2*a/x^4*A*b-1/4*a^2/x^4*C-1/x^2*a*A*c-1/2/x^2*A*b^2-1/x^2*C*a*b-1/6*a^2*A/x^6","A"
21,1,1622,290,0.065000," ","int(x^4*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x)","\frac{2 \sqrt{2}\, A a b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{2 \sqrt{2}\, A a b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, A \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{2 \sqrt{2}\, C \,a^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{2 \sqrt{2}\, C \,a^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{5 \sqrt{2}\, C a \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{5 \sqrt{2}\, C a \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, C \,b^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, C \,b^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A a \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A a \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{B a b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) c}-\frac{B a b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) c}+\frac{B \,b^{3} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c^{2}}+\frac{B \,b^{3} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c^{2}}+\frac{3 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{3 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{C \,x^{3}}{3 c}+\frac{\sqrt{-4 a c +b^{2}}\, B a \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right) c}-\frac{\sqrt{-4 a c +b^{2}}\, B a \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right) c}-\frac{\sqrt{-4 a c +b^{2}}\, B \,b^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c^{2}}+\frac{\sqrt{-4 a c +b^{2}}\, B \,b^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c^{2}}+\frac{B \,x^{2}}{2 c}+\frac{A x}{c}-\frac{C b x}{c^{2}}"," ",0,"1/3*C*x^3/c+1/2*B*x^2/c+1/2/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^3-1/2/c^2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*C-1/2/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^3+1/2/c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*C+2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*a*b-1/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*a*(-4*a*c+b^2)^(1/2)-2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*a*b-1/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*a*(-4*a*c+b^2)^(1/2)-1/c^2*b*C*x-1/2/c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^3-5/2/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*C*a+1/2/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2*(-4*a*c+b^2)^(1/2)+5/2/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*C*a-1/2/c/(4*a*c-b^2)*B*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*a*(-4*a*c+b^2)^(1/2)+A/c*x+1/2/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2*(-4*a*c+b^2)^(1/2)+3/2/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*a*b+3/2/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*a*b-1/2/c^2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^3+1/4/c^2/(4*a*c-b^2)*B*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*b^2*(-4*a*c+b^2)^(1/2)+1/2/c/(4*a*c-b^2)*B*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*a*(-4*a*c+b^2)^(1/2)-1/4/c^2/(4*a*c-b^2)*B*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*b^2*(-4*a*c+b^2)^(1/2)-1/c/(4*a*c-b^2)*B*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*a*b+2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a^2-2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a^2-1/c/(4*a*c-b^2)*B*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*a*b+1/4/c^2/(4*a*c-b^2)*B*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*b^3+1/4/c^2/(4*a*c-b^2)*B*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*b^3","B"
22,1,1171,233,0.054000," ","int(x^3*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x)","\frac{2 \sqrt{2}\, B a b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{2 \sqrt{2}\, B a b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, B \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, B \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{A a \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{4 a c -b^{2}}+\frac{A a \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{4 a c -b^{2}}-\frac{A \,b^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c}-\frac{A \,b^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B a \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B a \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{C a b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) c}-\frac{C a b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) c}+\frac{C \,b^{3} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c^{2}}+\frac{C \,b^{3} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c^{2}}+\frac{\sqrt{-4 a c +b^{2}}\, A b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c}-\frac{\sqrt{-4 a c +b^{2}}\, A b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c}+\frac{\sqrt{-4 a c +b^{2}}\, C a \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right) c}-\frac{\sqrt{-4 a c +b^{2}}\, C a \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right) c}-\frac{\sqrt{-4 a c +b^{2}}\, C \,b^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c^{2}}+\frac{\sqrt{-4 a c +b^{2}}\, C \,b^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c^{2}}+\frac{C \,x^{2}}{2 c}+\frac{B x}{c}"," ",0,"1/2*C*x^2/c+B/c*x+1/4/c/(4*a*c-b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b+1/(4*a*c-b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*a*A-1/4/c/(4*a*c-b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*b^2+1/2/c/(4*a*c-b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*a-1/4/c^2/(4*a*c-b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*b^2-1/c/(4*a*c-b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C*a*b+1/4/c^2/(4*a*c-b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*b^3*C-1/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*a+1/2/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*b^2+2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*B-1/2/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*B-1/4/c/(4*a*c-b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b+1/(4*a*c-b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*a*A-1/4/c/(4*a*c-b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*b^2-1/2/c/(4*a*c-b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*a+1/4/c^2/(4*a*c-b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*b^2-1/c/(4*a*c-b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C*a*b+1/4/c^2/(4*a*c-b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*b^3*C-1/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*a+1/2/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*b^2-2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*B+1/2/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*B","B"
23,1,1327,227,0.050000," ","int(x^2*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x)","-\frac{2 \sqrt{2}\, A a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, A a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, A \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C a b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C a b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, C \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{B a \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{4 a c -b^{2}}+\frac{B a \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{4 a c -b^{2}}-\frac{B \,b^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c}-\frac{B \,b^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c}-\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c}-\frac{\sqrt{2}\, \left(-4 a c +b^{2}\right) C b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, \left(-4 a c +b^{2}\right) C b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{C x}{c}"," ",0,"C*x/c+1/4/c/(4*a*c-b^2)*B*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b+1/(4*a*c-b^2)*B*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*a-1/4/c/(4*a*c-b^2)*B*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*b^2-1/2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b-2*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*a+1/2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2-1/4/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)*b-1/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*a+1/2/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^2+1/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*C*a-1/4/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*C-1/4/c/(4*a*c-b^2)*B*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*(-4*a*c+b^2)^(1/2)*b+1/(4*a*c-b^2)*B*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*a-1/4/c/(4*a*c-b^2)*B*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*b^2-1/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b+2*c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*a-1/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+1/4/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)*b-1/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*a+1/2/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^2-1/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*C*a+1/4/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*C","B"
24,1,728,180,0.040000," ","int(x*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x)","-\frac{2 \sqrt{2}\, B a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, B a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, B \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, B \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{C a \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{4 a c -b^{2}}+\frac{C a \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{4 a c -b^{2}}-\frac{C \,b^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c}-\frac{C \,b^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c}-\frac{\sqrt{-4 a c +b^{2}}\, A \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)}+\frac{\sqrt{-4 a c +b^{2}}\, A \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{8 a c -2 b^{2}}+\frac{\sqrt{-4 a c +b^{2}}\, C b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c}-\frac{\sqrt{-4 a c +b^{2}}\, C b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{4 \left(4 a c -b^{2}\right) c}"," ",0,"-1/2/(4*a*c-b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)+1/4/c/(4*a*c-b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*b+1/(4*a*c-b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*a*C-1/4/c/(4*a*c-b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*b^2*C-1/2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*b-2*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*B+1/2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*B+1/2/(4*a*c-b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)-1/4/c/(4*a*c-b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*b+1/(4*a*c-b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*a*C-1/4/c/(4*a*c-b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*b^2*C-1/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*b+2*c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*B-1/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*B","B"
25,1,616,171,0.025000," ","int((C*x^2+B*x+A)/(c*x^4+b*x^2+a),x)","-\frac{2 \sqrt{2}\, C a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, C a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, A c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, A c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, C b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{-4 a c +b^{2}}\, \sqrt{2}\, C b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{-4 a c +b^{2}}\, B \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)}+\frac{\sqrt{-4 a c +b^{2}}\, B \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{8 a c -2 b^{2}}"," ",0,"-1/2*(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*B*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))+c*(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A-2*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a+1/2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*b^2-1/2*(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*C+1/2*(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*B*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))+c*(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A+2*c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a-1/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*b^2-1/2*(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*C","B"
26,1,488,185,0.037000," ","int((C*x^2+B*x+A)/x/(c*x^4+b*x^2+a),x)","\frac{A \,b^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(16 a c -4 b^{2}\right) a}+\frac{A \,b^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(16 a c -4 b^{2}\right) a}-\frac{4 A c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{16 a c -4 b^{2}}-\frac{4 A c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{16 a c -4 b^{2}}+\frac{4 \sqrt{-4 a c +b^{2}}\, \sqrt{2}\, B c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{4 \sqrt{-4 a c +b^{2}}\, \sqrt{2}\, B c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{-4 a c +b^{2}}\, A b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(16 a c -4 b^{2}\right) a}-\frac{\sqrt{-4 a c +b^{2}}\, A b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(16 a c -4 b^{2}\right) a}-\frac{2 \sqrt{-4 a c +b^{2}}\, C \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{16 a c -4 b^{2}}+\frac{2 \sqrt{-4 a c +b^{2}}\, C \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{16 a c -4 b^{2}}+\frac{A \ln \left(x \right)}{a}"," ",0,"A/a*ln(x)-4*c/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A+1/a/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*b^2+1/a*(-4*a*c+b^2)^(1/2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*b-2*(-4*a*c+b^2)^(1/2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C+4*c*(-4*a*c+b^2)^(1/2)/(16*a*c-4*b^2)*B*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-4*c/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A+1/a/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*b^2-1/a*(-4*a*c+b^2)^(1/2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*b+2*(-4*a*c+b^2)^(1/2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C+4*c*(-4*a*c+b^2)^(1/2)/(16*a*c-4*b^2)*B*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)","B"
27,1,811,216,0.040000," ","int((C*x^2+B*x+A)/x^2/(c*x^4+b*x^2+a),x)","-\frac{2 \sqrt{2}\, A \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{2 \sqrt{2}\, A \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{8 \sqrt{2}\, A \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{8 \sqrt{2}\, A \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{2 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{2 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{B \,b^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(16 a c -4 b^{2}\right) a}+\frac{B \,b^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(16 a c -4 b^{2}\right) a}-\frac{4 B c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{16 a c -4 b^{2}}-\frac{4 B c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{16 a c -4 b^{2}}+\frac{4 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{4 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(16 a c -4 b^{2}\right) a}-\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(16 a c -4 b^{2}\right) a}+\frac{B \ln \left(x \right)}{a}-\frac{A}{a x}"," ",0,"-A/a/x+B/a*ln(x)+1/a/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*B*(-4*a*c+b^2)^(1/2)*b-4*c/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*B+1/a/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*b^2*B-2/a*c/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b+8*c^2/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A-2/a*c/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+4*c/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)-1/a/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*B*(-4*a*c+b^2)^(1/2)*b-4*c/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*B+1/a/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*b^2*B-2/a*c/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b-8*c^2/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A+2/a*c/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+4*c/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)","B"
28,1,1054,242,0.056000," ","int((C*x^2+B*x+A)/x^3/(c*x^4+b*x^2+a),x)","-\frac{4 \sqrt{2}\, B \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(32 a c -8 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, B \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(32 a c -8 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{16 \sqrt{2}\, B \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(32 a c -8 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{16 \sqrt{2}\, B \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(32 a c -8 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{8 A b c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(32 a c -8 b^{2}\right) a}+\frac{8 A b c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(32 a c -8 b^{2}\right) a}-\frac{2 A \,b^{3} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(32 a c -8 b^{2}\right) a^{2}}-\frac{2 A \,b^{3} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(32 a c -8 b^{2}\right) a^{2}}-\frac{4 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(32 a c -8 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{4 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(32 a c -8 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{2 C \,b^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(32 a c -8 b^{2}\right) a}+\frac{2 C \,b^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(32 a c -8 b^{2}\right) a}-\frac{8 C c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{32 a c -8 b^{2}}-\frac{8 C c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{32 a c -8 b^{2}}+\frac{4 \sqrt{-4 a c +b^{2}}\, A c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(32 a c -8 b^{2}\right) a}-\frac{4 \sqrt{-4 a c +b^{2}}\, A c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(32 a c -8 b^{2}\right) a}-\frac{2 \sqrt{-4 a c +b^{2}}\, A \,b^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(32 a c -8 b^{2}\right) a^{2}}+\frac{2 \sqrt{-4 a c +b^{2}}\, A \,b^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(32 a c -8 b^{2}\right) a^{2}}+\frac{2 \sqrt{-4 a c +b^{2}}\, C b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(32 a c -8 b^{2}\right) a}-\frac{2 \sqrt{-4 a c +b^{2}}\, C b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(32 a c -8 b^{2}\right) a}-\frac{A b \ln \left(x \right)}{a^{2}}+\frac{C \ln \left(x \right)}{a}-\frac{B}{a x}-\frac{A}{2 a \,x^{2}}"," ",0,"-1/2*A/a/x^2-B/a/x-A/a^2*b*ln(x)+1/a*ln(x)*C+8/a*c/(32*a*c-8*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*b-2/a^2/(32*a*c-8*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*b^3+4/a*c/(32*a*c-8*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)-2/a^2/(32*a*c-8*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b^2+2/a/(32*a*c-8*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*b-8*c/(32*a*c-8*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C+2/a/(32*a*c-8*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C*b^2-4/a*c/(32*a*c-8*b^2)*B*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*b+16*c^2/(32*a*c-8*b^2)*B*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-4/a*c/(32*a*c-8*b^2)*B*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2+8/a*c/(32*a*c-8*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*b-2/a^2/(32*a*c-8*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*b^3-4/a*c/(32*a*c-8*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)+2/a^2/(32*a*c-8*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b^2-2/a/(32*a*c-8*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*b-8*c/(32*a*c-8*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C+2/a/(32*a*c-8*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C*b^2-4/a*c/(32*a*c-8*b^2)*B*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*b-16*c^2/(32*a*c-8*b^2)*B*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+4/a*c/(32*a*c-8*b^2)*B*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2","B"
29,1,1429,363,0.062000," ","int(x^4*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x)","\frac{\sqrt{2}\, A a b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A a b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, A \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{6 \sqrt{2}\, C \,a^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{6 \sqrt{2}\, C \,a^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{5 \sqrt{2}\, C a \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{5 \sqrt{2}\, C a \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C \,b^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, C \,b^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{2 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{2 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{-4 a c +b^{2}}\, B a \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right)^{2}}+\frac{\sqrt{-4 a c +b^{2}}\, B a \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right)^{2}}+\frac{\frac{B a b}{2 \left(4 a c -b^{2}\right) c}-\frac{\left(2 a c -b^{2}\right) B \,x^{2}}{2 \left(4 a c -b^{2}\right) c}-\frac{\left(A b c +2 a c C -b^{2} C \right) x^{3}}{2 \left(4 a c -b^{2}\right) c}-\frac{\left(2 A c -b C \right) a x}{2 \left(4 a c -b^{2}\right) c}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2*(A*b*c+2*C*a*c-C*b^2)/(4*a*c-b^2)/c*x^3-1/2*B*(2*a*c-b^2)/(4*a*c-b^2)/c*x^2-1/2*a*(2*A*c-C*b)/(4*a*c-b^2)/c*x+1/2*a*b*B/c/(4*a*c-b^2))/(c*x^4+b*x^2+a)-1/(4*a*c-b^2)^2*B*(-4*a*c+b^2)^(1/2)*a*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))+1/(4*a*c-b^2)^2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*a+1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b^2+1/(4*a*c-b^2)^2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A*b-1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^3-2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*a*b+1/4/(4*a*c-b^2)^2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^3-6/(4*a*c-b^2)^2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a^2+5/2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a*b^2-1/4/(4*a*c-b^2)^2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*b^4+1/(4*a*c-b^2)^2*B*(-4*a*c+b^2)^(1/2)*a*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))+1/(4*a*c-b^2)^2*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*a+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b^2-1/(4*a*c-b^2)^2*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A*b+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^3-2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*a*b+1/4/(4*a*c-b^2)^2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^3+6/(4*a*c-b^2)^2*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a^2-5/2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a*b^2+1/4/(4*a*c-b^2)^2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*b^4","B"
30,1,831,298,0.044000," ","int(x^3*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x)","\frac{\sqrt{2}\, B a b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, B a b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, B \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, B \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{-4 a c +b^{2}}\, A b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}-\frac{\sqrt{-4 a c +b^{2}}\, A b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}-\frac{\sqrt{-4 a c +b^{2}}\, C a \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right)^{2}}+\frac{\sqrt{-4 a c +b^{2}}\, C a \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right)^{2}}+\frac{-\frac{B b \,x^{3}}{2 \left(4 a c -b^{2}\right)}-\frac{B a x}{4 a c -b^{2}}-\frac{\left(A b c +2 a c C -b^{2} C \right) x^{2}}{2 \left(4 a c -b^{2}\right) c}-\frac{\left(2 A c -b C \right) a}{2 \left(4 a c -b^{2}\right) c}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2*b*B/(4*a*c-b^2)*x^3-1/2*(A*b*c+2*C*a*c-C*b^2)/(4*a*c-b^2)/c*x^2-a*B/(4*a*c-b^2)*x-1/2*a*(2*A*c-C*b)/(4*a*c-b^2)/c)/(c*x^4+b*x^2+a)+1/2/(4*a*c-b^2)^2*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b-1/(4*a*c-b^2)^2*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*a+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*a+1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*B-1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*B-1/2/(4*a*c-b^2)^2*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b+1/(4*a*c-b^2)^2*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*a+c/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*a+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*b^2-c/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*B+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*B","B"
31,1,1119,306,0.055000," ","int(x^2*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x)","-\frac{2 \sqrt{2}\, A a \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, A a \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, A \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C a b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C a b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}-\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}+\frac{-\frac{B b \,x^{2}}{2 \left(4 a c -b^{2}\right)}+\frac{\left(2 A c -b C \right) x^{3}}{8 a c -2 b^{2}}-\frac{B a}{4 a c -b^{2}}+\frac{\left(A b -2 a C \right) x}{8 a c -2 b^{2}}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(1/2*(2*A*c-C*b)/(4*a*c-b^2)*x^3-1/2*b*B/(4*a*c-b^2)*x^2+1/2*(A*b-2*C*a)/(4*a*c-b^2)*x-a*B/(4*a*c-b^2))/(c*x^4+b*x^2+a)+1/2/(4*a*c-b^2)^2*B*(-4*a*c+b^2)^(1/2)*b*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))-c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b-2*c^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A+1/2*c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*a+1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a*b-1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*C-1/2/(4*a*c-b^2)^2*B*(-4*a*c+b^2)^(1/2)*b*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))-c/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b+2*c^2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A-1/2*c/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*a+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^2-c/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a*b+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*C","B"
32,1,1344,272,0.177000," ","int(x*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x)","-\frac{2 \sqrt{2}\, B a \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, B a \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, B \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, B \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 B a c x}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}+\frac{2 B a c x}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{B \,b^{2} x}{2 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{B \,b^{2} x}{2 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 A a c}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}+\frac{2 A a c}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{A \,b^{2}}{2 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{A \,b^{2}}{2 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{\sqrt{-4 a c +b^{2}}\, A c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right)^{2}}+\frac{\sqrt{-4 a c +b^{2}}\, A c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right)^{2}}-\frac{C a b}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{C a b}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}+\frac{C \,b^{3}}{4 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) c}+\frac{C \,b^{3}}{4 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) c}+\frac{\sqrt{-4 a c +b^{2}}\, C b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}-\frac{\sqrt{-4 a c +b^{2}}\, C b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}+\frac{\sqrt{-4 a c +b^{2}}\, C a}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{\sqrt{-4 a c +b^{2}}\, C a}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{\sqrt{-4 a c +b^{2}}\, C \,b^{2}}{4 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) c}+\frac{\sqrt{-4 a c +b^{2}}\, C \,b^{2}}{4 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) c}"," ",0,"-2*c^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*B+1/2*c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*B+2*c^2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*B-1/2*c/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*B-1/2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*A*b^2-1/2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*A*b^2-c/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*b*B-c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*(-4*a*c+b^2)^(1/2)*b*B+1/4/c/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*b^3*C+c/(4*a*c-b^2)^2*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)+2*c/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*A*a+1/4/c/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*b^3*C-c/(4*a*c-b^2)^2*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)+2*c/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*A*a-1/2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*B*x*b^2+1/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*C*(-4*a*c+b^2)^(1/2)*a-1/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*C*a*b+1/2/(4*a*c-b^2)^2*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*b-1/2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*B*x*b^2-1/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*C*(-4*a*c+b^2)^(1/2)*a-1/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*C*a*b-1/2/(4*a*c-b^2)^2*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*b+2*c/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*B*a*x-1/4/c/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*C*(-4*a*c+b^2)^(1/2)*b^2+2*c/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*B*a*x+1/4/c/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*C*(-4*a*c+b^2)^(1/2)*b^2","B"
33,1,1813,320,0.151000," ","int((C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x)","-\frac{\sqrt{2}\, A \,b^{3} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, A \,b^{3} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, A b \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A b \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{2 \sqrt{2}\, C a \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, C a \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{A \,b^{3} x}{4 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}+\frac{A \,b^{3} x}{4 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{A b c x}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{A b c x}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}+\frac{3 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 C a c x}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}+\frac{2 C a c x}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{C \,b^{2} x}{2 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{C \,b^{2} x}{2 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{-4 a c +b^{2}}\, A \,b^{2} x}{4 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}-\frac{\sqrt{-4 a c +b^{2}}\, A \,b^{2} x}{4 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}-\frac{\sqrt{-4 a c +b^{2}}\, A c x}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}+\frac{\sqrt{-4 a c +b^{2}}\, A c x}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}+\frac{2 B a c}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}+\frac{2 B a c}{\left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{B \,b^{2}}{2 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{B \,b^{2}}{2 \left(4 a c -b^{2}\right)^{2} \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{\sqrt{-4 a c +b^{2}}\, B c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right)^{2}}+\frac{\sqrt{-4 a c +b^{2}}\, B c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right)^{2}}"," ",0,"-1/2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*B*b^2-1/2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*B*b^2-1/2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*x*C*b^2+2*c/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*B*a-c/(4*a*c-b^2)^2*B*(-4*a*c+b^2)^(1/2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))+2*c/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*B*a+c/(4*a*c-b^2)^2*B*(-4*a*c+b^2)^(1/2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))+3*c^2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)-c^2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b+2*c^2/(4*a*c-b^2)^2*a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C-1/4*c/(4*a*c-b^2)^2/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^3-c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b+1/4*c/(4*a*c-b^2)^2/a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^3-c/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b+1/4/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)/a*x*A*b^3+1/4/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)/a*x*A*b^3-c/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*x*A*(-4*a*c+b^2)^(1/2)-c/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*A*b*x+2*c/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*a*C*x+c/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*x*A*(-4*a*c+b^2)^(1/2)-c/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*A*b*x+2*c/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*a*C*x-1/2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*x*C*b^2-1/4*c/(4*a*c-b^2)^2/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b^2-1/4*c/(4*a*c-b^2)^2/a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b^2-1/2*c/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*b^2+3*c^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)+c^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b-2*c^2/(4*a*c-b^2)^2*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C+1/2*c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*b^2+1/4/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)/a*x*A*(-4*a*c+b^2)^(1/2)*b^2-1/4/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)/a*x*A*(-4*a*c+b^2)^(1/2)*b^2","B"
34,1,1603,347,0.063000," ","int((C*x^2+B*x+A)/x/(c*x^4+b*x^2+a)^2,x)","-\frac{\sqrt{2}\, B \,b^{3} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, B \,b^{3} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{B b c \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{4 \sqrt{2}\, B b \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{4 \sqrt{2}\, B b \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{8 A \,b^{2} c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}+\frac{8 A \,b^{2} c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}-\frac{A b c \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{A \,b^{4} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}-\frac{A \,b^{4} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}-\frac{16 A \,c^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right)}-\frac{16 A \,c^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right)}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{12 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{12 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{C c \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{6 \sqrt{-4 a c +b^{2}}\, A b c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}-\frac{6 \sqrt{-4 a c +b^{2}}\, A b c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}-\frac{\sqrt{-4 a c +b^{2}}\, A \,b^{3} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}+\frac{\sqrt{-4 a c +b^{2}}\, A \,b^{3} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}-\frac{B \,b^{2} x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{B c x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{4 \sqrt{-4 a c +b^{2}}\, C c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right)}+\frac{4 \sqrt{-4 a c +b^{2}}\, C c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right)}-\frac{A \,b^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{A c}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{C b}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{A \ln \left(x \right)}{a^{2}}"," ",0,"-1/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*b^2-1/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*b^2-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*B/a*b^2*x-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*B/a*b*c*x^3+A/a^2*ln(x)+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*C*b+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A*c-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A/a*b*c*x^2-1/a^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*b^4-1/a^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*b^4-4*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)+4*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)-6/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b+12*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)+4*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*B-16*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A-16*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A-1/a^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b^3+8/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*b^2+1/a^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b^3+8/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*b^2-1/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*b^3+1/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*b^3-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A/a*b^2+1/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*C+12*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)-4*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*B+6/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*B*c*x","B"
35,1,2398,452,0.085000," ","int((C*x^2+B*x+A)/x^2/(c*x^4+b*x^2+a)^2,x)","-\frac{22 \sqrt{2}\, A \,b^{2} c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{22 \sqrt{2}\, A \,b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{A \,c^{2} x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{3 \sqrt{2}\, A \,b^{4} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, A \,b^{4} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{A \,b^{2} c \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{40 \sqrt{2}\, A \,c^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{40 \sqrt{2}\, A \,c^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C \,b^{3} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, C \,b^{3} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{C b c \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{4 \sqrt{2}\, C b \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{4 \sqrt{2}\, C b \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{16 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{16 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{3 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A \,b^{3} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{3 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A \,b^{3} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{8 B \,b^{2} c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}+\frac{8 B \,b^{2} c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}-\frac{B b c \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{B \,b^{4} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}-\frac{B \,b^{4} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}-\frac{16 B \,c^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right)}-\frac{16 B \,c^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right)}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{12 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{12 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 A b c x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{A \,b^{3} x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{6 \sqrt{-4 a c +b^{2}}\, B b c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}-\frac{6 \sqrt{-4 a c +b^{2}}\, B b c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}-\frac{\sqrt{-4 a c +b^{2}}\, B \,b^{3} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}+\frac{\sqrt{-4 a c +b^{2}}\, B \,b^{3} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}-\frac{C \,b^{2} x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{C c x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{B \,b^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{B c}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{B \ln \left(x \right)}{a^{2}}-\frac{A}{a^{2} x}"," ",0,"-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*B/a*b^2-1/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^2-1/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^2-16/a*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b+3/a^2*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b^3+3/a^2*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b^3-16/a*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b+B/a^2*ln(x)-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A/a*c^2*x^3+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A/a^2*b^3*x+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A/a^2*b^2*c*x^3-3/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A/a*b*c*x+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*B*c-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*B/a*b*c*x^2-1/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*b^3+22/a*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2-3/a^2*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^4+3/a^2*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^4-22/a*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+1/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*b^3+6/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*B*(-4*a*c+b^2)^(1/2)*b-6/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*B*(-4*a*c+b^2)^(1/2)*b+12*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)+12*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)-4*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*b+4*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*b+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*c*C-1/2/a/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*C*b-1/a^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*B*(-4*a*c+b^2)^(1/2)*b^3+1/a^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*B*(-4*a*c+b^2)^(1/2)*b^3+8/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*b^2*B+8/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*b^2*B+40*c^3/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A-40*c^3/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A-16*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*B-16*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*B-1/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*C*b^2-1/a^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*b^4*B-1/a^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*b^4*B-A/a^2/x","B"
36,1,2512,473,0.096000," ","int((C*x^2+B*x+A)/x^3/(c*x^4+b*x^2+a)^2,x)","-\frac{22 \sqrt{2}\, B \,b^{2} c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{22 \sqrt{2}\, B \,b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{B \,c^{2} x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{3 \sqrt{2}\, B \,b^{4} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, B \,b^{4} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{B \,b^{2} c \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{40 \sqrt{2}\, B \,c^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{40 \sqrt{2}\, B \,c^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{32 A b \,c^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}+\frac{32 A b \,c^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}-\frac{A \,c^{2} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{16 A \,b^{3} c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}-\frac{16 A \,b^{3} c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}+\frac{A \,b^{2} c \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{2 A \,b^{5} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{3}}+\frac{2 A \,b^{5} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{3}}-\frac{16 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B b \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{16 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B b \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{3 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B \,b^{3} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{3 \sqrt{2}\, \sqrt{-4 a c +b^{2}}\, B \,b^{3} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{8 C \,b^{2} c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}+\frac{8 C \,b^{2} c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}-\frac{C b c \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{C \,b^{4} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}-\frac{C \,b^{4} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}-\frac{16 C \,c^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right)}-\frac{16 C \,c^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right)}+\frac{12 \sqrt{-4 a c +b^{2}}\, A \,c^{2} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}-\frac{12 \sqrt{-4 a c +b^{2}}\, A \,c^{2} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}-\frac{12 \sqrt{-4 a c +b^{2}}\, A \,b^{2} c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}+\frac{12 \sqrt{-4 a c +b^{2}}\, A \,b^{2} c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}+\frac{2 \sqrt{-4 a c +b^{2}}\, A \,b^{4} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{3}}-\frac{2 \sqrt{-4 a c +b^{2}}\, A \,b^{4} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{3}}-\frac{3 B b c x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{B \,b^{3} x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{6 \sqrt{-4 a c +b^{2}}\, C b c \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}-\frac{6 \sqrt{-4 a c +b^{2}}\, C b c \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a}-\frac{\sqrt{-4 a c +b^{2}}\, C \,b^{3} \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}+\frac{\sqrt{-4 a c +b^{2}}\, C \,b^{3} \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{\left(4 a c -b^{2}\right) \left(16 a c -4 b^{2}\right) a^{2}}-\frac{3 A b c}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{A \,b^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{C \,b^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{C c}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{2 A b \ln \left(x \right)}{a^{3}}+\frac{C \ln \left(x \right)}{a^{2}}-\frac{B}{a^{2} x}-\frac{A}{2 a^{2} x^{2}}"," ",0,"1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A/a^2*b^3-1/2*A/a^2/x^2-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A/a*c^2*x^2-3/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A/a*b*c+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*B/a^2*b^2*c*x^3-3/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*B/a*b*c*x+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*c*C-2*A/a^3*b*ln(x)+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A/a^2*b^2*c*x^2+6/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*b-12/a^2*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b^2-6/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*b+12/a^2*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b^2+2/a^3/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*b^5+2/a^3/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*b^5-1/a^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C*b^4-1/a^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C*b^4+1/a^2*ln(x)*C-16*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C-16*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C-B/a^2/x-16/a*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*b+3/a^2*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*b^3+3/a^2*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*b^3-16/a*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*(-4*a*c+b^2)^(1/2)*b-22/a*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*b^2-3/a^2*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*b^4+3/a^2*c/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*b^4+22/a*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*b^2-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*B/a*c^2*x^3+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*B/a^2*b^3*x-1/2/a/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*C*b-40*c^3/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B+40*c^3/(4*a*c-b^2)/(16*a*c-4*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B+12/a*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)+2/a^3/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b^4+32/a*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*b-16/a^2*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*b^3+8/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C*b^2-16/a^2*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*A*b^3+8/a*c/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C*b^2-12/a*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)-2/a^3/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*(-4*a*c+b^2)^(1/2)*b^4+32/a*c^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*A*b+1/a^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*b^3-1/a^2/(4*a*c-b^2)/(16*a*c-4*b^2)*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))*C*(-4*a*c+b^2)^(1/2)*b^3-1/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*C*b^2","B"
37,1,5520,399,0.013000," ","int((d*x)^m*(C*x^2+B*x+A)*(c*x^4+b*x^2+a)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
38,1,2187,260,0.010000," ","int((d*x)^m*(C*x^2+B*x+A)*(c*x^4+b*x^2+a)^2,x)","\frac{\left(C \,c^{2} m^{10} x^{10}+B \,c^{2} m^{10} x^{9}+55 C \,c^{2} m^{9} x^{10}+A \,c^{2} m^{10} x^{8}+56 B \,c^{2} m^{9} x^{9}+2 C b c \,m^{10} x^{8}+1320 C \,c^{2} m^{8} x^{10}+57 A \,c^{2} m^{9} x^{8}+2 B b c \,m^{10} x^{7}+1365 B \,c^{2} m^{8} x^{9}+114 C b c \,m^{9} x^{8}+18150 C \,c^{2} m^{7} x^{10}+2 A b c \,m^{10} x^{6}+1412 A \,c^{2} m^{8} x^{8}+116 B b c \,m^{9} x^{7}+19020 B \,c^{2} m^{7} x^{9}+2 C a c \,m^{10} x^{6}+C \,b^{2} m^{10} x^{6}+2824 C b c \,m^{8} x^{8}+157773 C \,c^{2} m^{6} x^{10}+118 A b c \,m^{9} x^{6}+19962 A \,c^{2} m^{7} x^{8}+2 B a c \,m^{10} x^{5}+B \,b^{2} m^{10} x^{5}+2922 B b c \,m^{8} x^{7}+167223 B \,c^{2} m^{6} x^{9}+118 C a c \,m^{9} x^{6}+59 C \,b^{2} m^{9} x^{6}+39924 C b c \,m^{7} x^{8}+902055 C \,c^{2} m^{5} x^{10}+2 A a c \,m^{10} x^{4}+A \,b^{2} m^{10} x^{4}+3024 A b c \,m^{8} x^{6}+177765 A \,c^{2} m^{6} x^{8}+120 B a c \,m^{9} x^{5}+60 B \,b^{2} m^{9} x^{5}+41964 B b c \,m^{7} x^{7}+965328 B \,c^{2} m^{5} x^{9}+2 C a b \,m^{10} x^{4}+3024 C a c \,m^{8} x^{6}+1512 C \,b^{2} m^{8} x^{6}+355530 C b c \,m^{6} x^{8}+3416930 C \,c^{2} m^{4} x^{10}+122 A a c \,m^{9} x^{4}+61 A \,b^{2} m^{9} x^{4}+44172 A b c \,m^{7} x^{6}+1037673 A \,c^{2} m^{5} x^{8}+2 B a b \,m^{10} x^{3}+3130 B a c \,m^{8} x^{5}+1565 B \,b^{2} m^{8} x^{5}+379134 B b c \,m^{6} x^{7}+3686255 B \,c^{2} m^{4} x^{9}+122 C a b \,m^{9} x^{4}+44172 C a c \,m^{7} x^{6}+22086 C \,b^{2} m^{7} x^{6}+2075346 C b c \,m^{5} x^{8}+8409500 C \,c^{2} m^{3} x^{10}+2 A a b \,m^{10} x^{2}+3240 A a c \,m^{8} x^{4}+1620 A \,b^{2} m^{8} x^{4}+405642 A b c \,m^{6} x^{6}+4000478 A \,c^{2} m^{4} x^{8}+124 B a b \,m^{9} x^{3}+46560 B a c \,m^{7} x^{5}+23280 B \,b^{2} m^{7} x^{5}+2242044 B b c \,m^{5} x^{7}+9133180 B \,c^{2} m^{3} x^{9}+C \,a^{2} m^{10} x^{2}+3240 C a b \,m^{8} x^{4}+405642 C a c \,m^{6} x^{6}+202821 C \,b^{2} m^{6} x^{6}+8000956 C b c \,m^{4} x^{8}+12753576 C \,c^{2} m^{2} x^{10}+126 A a b \,m^{9} x^{2}+49140 A a c \,m^{7} x^{4}+24570 A \,b^{2} m^{7} x^{4}+2435622 A b c \,m^{5} x^{6}+9991428 A \,c^{2} m^{3} x^{8}+B \,a^{2} m^{10} x +3354 B a b \,m^{8} x^{3}+435486 B a c \,m^{6} x^{5}+217743 B \,b^{2} m^{6} x^{5}+8742718 B b c \,m^{4} x^{7}+13926276 B \,c^{2} m^{2} x^{9}+63 C \,a^{2} m^{9} x^{2}+49140 C a b \,m^{7} x^{4}+2435622 C a c \,m^{5} x^{6}+1217811 C \,b^{2} m^{5} x^{6}+19982856 C b c \,m^{3} x^{8}+10628640 C \,c^{2} m \,x^{10}+A \,a^{2} m^{10}+3472 A a b \,m^{8} x^{2}+469146 A a c \,m^{6} x^{4}+234573 A \,b^{2} m^{6} x^{4}+9629716 A b c \,m^{4} x^{6}+15335224 A \,c^{2} m^{2} x^{8}+64 B \,a^{2} m^{9} x +51924 B a b \,m^{7} x^{3}+2662200 B a c \,m^{5} x^{5}+1331100 B \,b^{2} m^{5} x^{5}+22049716 B b c \,m^{3} x^{7}+11655216 B \,c^{2} m \,x^{9}+1736 C \,a^{2} m^{8} x^{2}+469146 C a b \,m^{6} x^{4}+9629716 C a c \,m^{4} x^{6}+4814858 C \,b^{2} m^{4} x^{6}+30670448 C b c \,m^{2} x^{8}+3628800 C \,c^{2} x^{10}+65 A \,a^{2} m^{9}+54924 A a b \,m^{7} x^{2}+2929386 A a c \,m^{5} x^{4}+1464693 A \,b^{2} m^{5} x^{4}+24583448 A b c \,m^{3} x^{6}+12900960 A \,c^{2} m \,x^{8}+1797 B \,a^{2} m^{8} x +507150 B a b \,m^{6} x^{3}+10705870 B a c \,m^{4} x^{5}+5352935 B \,b^{2} m^{4} x^{5}+34118424 B b c \,m^{2} x^{7}+3991680 B \,c^{2} x^{9}+27462 C \,a^{2} m^{7} x^{2}+2929386 C a b \,m^{5} x^{4}+24583448 C a c \,m^{3} x^{6}+12291724 C \,b^{2} m^{3} x^{6}+25801920 C b c m \,x^{8}+1860 A \,a^{2} m^{8}+550074 A a b \,m^{6} x^{2}+12032140 A a c \,m^{4} x^{4}+6016070 A \,b^{2} m^{4} x^{4}+38432016 A b c \,m^{2} x^{6}+4435200 A \,c^{2} x^{8}+29076 B \,a^{2} m^{7} x +3246516 B a b \,m^{5} x^{3}+27756240 B a c \,m^{3} x^{5}+13878120 B \,b^{2} m^{3} x^{5}+28888560 B b c m \,x^{7}+275037 C \,a^{2} m^{6} x^{2}+12032140 C a b \,m^{4} x^{4}+38432016 C a c \,m^{2} x^{6}+19216008 C \,b^{2} m^{2} x^{6}+8870400 C b c \,x^{8}+30810 A \,a^{2} m^{7}+3624894 A a b \,m^{5} x^{2}+31830760 A a c \,m^{3} x^{4}+15915380 A \,b^{2} m^{3} x^{4}+32811840 A b c m \,x^{6}+299271 B \,a^{2} m^{6} x +13693006 B a b \,m^{4} x^{3}+43978712 B a c \,m^{2} x^{5}+21989356 B \,b^{2} m^{2} x^{5}+9979200 B b c \,x^{7}+1812447 C \,a^{2} m^{5} x^{2}+31830760 C a b \,m^{3} x^{4}+32811840 C a c m \,x^{6}+16405920 C \,b^{2} m \,x^{6}+326613 A \,a^{2} m^{6}+15804388 A a b \,m^{4} x^{2}+51362352 A a c \,m^{2} x^{4}+25681176 A \,b^{2} m^{2} x^{4}+11404800 A b c \,x^{6}+2039016 B \,a^{2} m^{5} x +37219436 B a b \,m^{3} x^{3}+37963680 B a c m \,x^{5}+18981840 B \,b^{2} m \,x^{5}+7902194 C \,a^{2} m^{4} x^{2}+51362352 C a b \,m^{2} x^{4}+11404800 C a c \,x^{6}+5702400 C \,b^{2} x^{6}+2310945 A \,a^{2} m^{5}+44578296 A a b \,m^{3} x^{2}+45024192 A a c m \,x^{4}+22512096 A \,b^{2} m \,x^{4}+9261503 B \,a^{2} m^{4} x +61638408 B a b \,m^{2} x^{3}+13305600 B a c \,x^{5}+6652800 B \,b^{2} x^{5}+22289148 C \,a^{2} m^{3} x^{2}+45024192 C a b m \,x^{4}+11028590 A \,a^{2} m^{4}+76781264 A a b \,m^{2} x^{2}+15966720 A a c \,x^{4}+7983360 A \,b^{2} x^{4}+27472724 B \,a^{2} m^{3} x +55282320 B a b m \,x^{3}+38390632 C \,a^{2} m^{2} x^{2}+15966720 C a b \,x^{4}+34967140 A \,a^{2} m^{3}+71492160 A a b m \,x^{2}+50312628 B \,a^{2} m^{2} x +19958400 B a b \,x^{3}+35746080 C \,a^{2} m \,x^{2}+70290936 A \,a^{2} m^{2}+26611200 A a b \,x^{2}+50292720 B \,a^{2} m x +13305600 C \,a^{2} x^{2}+80627040 A \,a^{2} m +19958400 B \,a^{2} x +39916800 A \,a^{2}\right) x \left(d x \right)^{m}}{\left(m +11\right) \left(m +10\right) \left(m +9\right) \left(m +8\right) \left(m +7\right) \left(m +6\right) \left(m +5\right) \left(m +4\right) \left(m +3\right) \left(m +2\right) \left(m +1\right)}"," ",0,"x*(C*c^2*m^10*x^10+B*c^2*m^10*x^9+55*C*c^2*m^9*x^10+A*c^2*m^10*x^8+56*B*c^2*m^9*x^9+2*C*b*c*m^10*x^8+1320*C*c^2*m^8*x^10+57*A*c^2*m^9*x^8+2*B*b*c*m^10*x^7+1365*B*c^2*m^8*x^9+114*C*b*c*m^9*x^8+18150*C*c^2*m^7*x^10+2*A*b*c*m^10*x^6+1412*A*c^2*m^8*x^8+116*B*b*c*m^9*x^7+19020*B*c^2*m^7*x^9+2*C*a*c*m^10*x^6+C*b^2*m^10*x^6+2824*C*b*c*m^8*x^8+157773*C*c^2*m^6*x^10+118*A*b*c*m^9*x^6+19962*A*c^2*m^7*x^8+2*B*a*c*m^10*x^5+B*b^2*m^10*x^5+2922*B*b*c*m^8*x^7+167223*B*c^2*m^6*x^9+118*C*a*c*m^9*x^6+59*C*b^2*m^9*x^6+39924*C*b*c*m^7*x^8+902055*C*c^2*m^5*x^10+2*A*a*c*m^10*x^4+A*b^2*m^10*x^4+3024*A*b*c*m^8*x^6+177765*A*c^2*m^6*x^8+120*B*a*c*m^9*x^5+60*B*b^2*m^9*x^5+41964*B*b*c*m^7*x^7+965328*B*c^2*m^5*x^9+2*C*a*b*m^10*x^4+3024*C*a*c*m^8*x^6+1512*C*b^2*m^8*x^6+355530*C*b*c*m^6*x^8+3416930*C*c^2*m^4*x^10+122*A*a*c*m^9*x^4+61*A*b^2*m^9*x^4+44172*A*b*c*m^7*x^6+1037673*A*c^2*m^5*x^8+2*B*a*b*m^10*x^3+3130*B*a*c*m^8*x^5+1565*B*b^2*m^8*x^5+379134*B*b*c*m^6*x^7+3686255*B*c^2*m^4*x^9+122*C*a*b*m^9*x^4+44172*C*a*c*m^7*x^6+22086*C*b^2*m^7*x^6+2075346*C*b*c*m^5*x^8+8409500*C*c^2*m^3*x^10+2*A*a*b*m^10*x^2+3240*A*a*c*m^8*x^4+1620*A*b^2*m^8*x^4+405642*A*b*c*m^6*x^6+4000478*A*c^2*m^4*x^8+124*B*a*b*m^9*x^3+46560*B*a*c*m^7*x^5+23280*B*b^2*m^7*x^5+2242044*B*b*c*m^5*x^7+9133180*B*c^2*m^3*x^9+C*a^2*m^10*x^2+3240*C*a*b*m^8*x^4+405642*C*a*c*m^6*x^6+202821*C*b^2*m^6*x^6+8000956*C*b*c*m^4*x^8+12753576*C*c^2*m^2*x^10+126*A*a*b*m^9*x^2+49140*A*a*c*m^7*x^4+24570*A*b^2*m^7*x^4+2435622*A*b*c*m^5*x^6+9991428*A*c^2*m^3*x^8+B*a^2*m^10*x+3354*B*a*b*m^8*x^3+435486*B*a*c*m^6*x^5+217743*B*b^2*m^6*x^5+8742718*B*b*c*m^4*x^7+13926276*B*c^2*m^2*x^9+63*C*a^2*m^9*x^2+49140*C*a*b*m^7*x^4+2435622*C*a*c*m^5*x^6+1217811*C*b^2*m^5*x^6+19982856*C*b*c*m^3*x^8+10628640*C*c^2*m*x^10+A*a^2*m^10+3472*A*a*b*m^8*x^2+469146*A*a*c*m^6*x^4+234573*A*b^2*m^6*x^4+9629716*A*b*c*m^4*x^6+15335224*A*c^2*m^2*x^8+64*B*a^2*m^9*x+51924*B*a*b*m^7*x^3+2662200*B*a*c*m^5*x^5+1331100*B*b^2*m^5*x^5+22049716*B*b*c*m^3*x^7+11655216*B*c^2*m*x^9+1736*C*a^2*m^8*x^2+469146*C*a*b*m^6*x^4+9629716*C*a*c*m^4*x^6+4814858*C*b^2*m^4*x^6+30670448*C*b*c*m^2*x^8+3628800*C*c^2*x^10+65*A*a^2*m^9+54924*A*a*b*m^7*x^2+2929386*A*a*c*m^5*x^4+1464693*A*b^2*m^5*x^4+24583448*A*b*c*m^3*x^6+12900960*A*c^2*m*x^8+1797*B*a^2*m^8*x+507150*B*a*b*m^6*x^3+10705870*B*a*c*m^4*x^5+5352935*B*b^2*m^4*x^5+34118424*B*b*c*m^2*x^7+3991680*B*c^2*x^9+27462*C*a^2*m^7*x^2+2929386*C*a*b*m^5*x^4+24583448*C*a*c*m^3*x^6+12291724*C*b^2*m^3*x^6+25801920*C*b*c*m*x^8+1860*A*a^2*m^8+550074*A*a*b*m^6*x^2+12032140*A*a*c*m^4*x^4+6016070*A*b^2*m^4*x^4+38432016*A*b*c*m^2*x^6+4435200*A*c^2*x^8+29076*B*a^2*m^7*x+3246516*B*a*b*m^5*x^3+27756240*B*a*c*m^3*x^5+13878120*B*b^2*m^3*x^5+28888560*B*b*c*m*x^7+275037*C*a^2*m^6*x^2+12032140*C*a*b*m^4*x^4+38432016*C*a*c*m^2*x^6+19216008*C*b^2*m^2*x^6+8870400*C*b*c*x^8+30810*A*a^2*m^7+3624894*A*a*b*m^5*x^2+31830760*A*a*c*m^3*x^4+15915380*A*b^2*m^3*x^4+32811840*A*b*c*m*x^6+299271*B*a^2*m^6*x+13693006*B*a*b*m^4*x^3+43978712*B*a*c*m^2*x^5+21989356*B*b^2*m^2*x^5+9979200*B*b*c*x^7+1812447*C*a^2*m^5*x^2+31830760*C*a*b*m^3*x^4+32811840*C*a*c*m*x^6+16405920*C*b^2*m*x^6+326613*A*a^2*m^6+15804388*A*a*b*m^4*x^2+51362352*A*a*c*m^2*x^4+25681176*A*b^2*m^2*x^4+11404800*A*b*c*x^6+2039016*B*a^2*m^5*x+37219436*B*a*b*m^3*x^3+37963680*B*a*c*m*x^5+18981840*B*b^2*m*x^5+7902194*C*a^2*m^4*x^2+51362352*C*a*b*m^2*x^4+11404800*C*a*c*x^6+5702400*C*b^2*x^6+2310945*A*a^2*m^5+44578296*A*a*b*m^3*x^2+45024192*A*a*c*m*x^4+22512096*A*b^2*m*x^4+9261503*B*a^2*m^4*x+61638408*B*a*b*m^2*x^3+13305600*B*a*c*x^5+6652800*B*b^2*x^5+22289148*C*a^2*m^3*x^2+45024192*C*a*b*m*x^4+11028590*A*a^2*m^4+76781264*A*a*b*m^2*x^2+15966720*A*a*c*x^4+7983360*A*b^2*x^4+27472724*B*a^2*m^3*x+55282320*B*a*b*m*x^3+38390632*C*a^2*m^2*x^2+15966720*C*a*b*x^4+34967140*A*a^2*m^3+71492160*A*a*b*m*x^2+50312628*B*a^2*m^2*x+19958400*B*a*b*x^3+35746080*C*a^2*m*x^2+70290936*A*a^2*m^2+26611200*A*a*b*x^2+50292720*B*a^2*m*x+13305600*C*a^2*x^2+80627040*A*a^2*m+19958400*B*a^2*x+39916800*A*a^2)*(d*x)^m/(m+11)/(10+m)/(m+9)/(8+m)/(m+7)/(6+m)/(m+5)/(4+m)/(m+3)/(2+m)/(m+1)","B"
39,1,585,137,0.005000," ","int((d*x)^m*(C*x^2+B*x+A)*(c*x^4+b*x^2+a),x)","\frac{\left(C c \,m^{6} x^{6}+B c \,m^{6} x^{5}+21 C c \,m^{5} x^{6}+A c \,m^{6} x^{4}+22 B c \,m^{5} x^{5}+C b \,m^{6} x^{4}+175 C c \,m^{4} x^{6}+23 A c \,m^{5} x^{4}+B b \,m^{6} x^{3}+190 B c \,m^{4} x^{5}+23 C b \,m^{5} x^{4}+735 C c \,m^{3} x^{6}+A b \,m^{6} x^{2}+207 A c \,m^{4} x^{4}+24 B b \,m^{5} x^{3}+820 B c \,m^{3} x^{5}+C a \,m^{6} x^{2}+207 C b \,m^{4} x^{4}+1624 C c \,m^{2} x^{6}+25 A b \,m^{5} x^{2}+925 A c \,m^{3} x^{4}+B a \,m^{6} x +226 B b \,m^{4} x^{3}+1849 B c \,m^{2} x^{5}+25 C a \,m^{5} x^{2}+925 C b \,m^{3} x^{4}+1764 C c m \,x^{6}+A a \,m^{6}+247 A b \,m^{4} x^{2}+2144 A c \,m^{2} x^{4}+26 B a \,m^{5} x +1056 B b \,m^{3} x^{3}+2038 B c m \,x^{5}+247 C a \,m^{4} x^{2}+2144 C b \,m^{2} x^{4}+720 C c \,x^{6}+27 A a \,m^{5}+1219 A b \,m^{3} x^{2}+2412 A c m \,x^{4}+270 B a \,m^{4} x +2545 B b \,m^{2} x^{3}+840 B c \,x^{5}+1219 C a \,m^{3} x^{2}+2412 C b m \,x^{4}+295 A a \,m^{4}+3112 A b \,m^{2} x^{2}+1008 A c \,x^{4}+1420 B a \,m^{3} x +2952 B b m \,x^{3}+3112 C a \,m^{2} x^{2}+1008 C b \,x^{4}+1665 A a \,m^{3}+3796 A b m \,x^{2}+3929 B a \,m^{2} x +1260 B b \,x^{3}+3796 C a m \,x^{2}+5104 A a \,m^{2}+1680 A b \,x^{2}+5274 B a m x +1680 C a \,x^{2}+8028 A a m +2520 B a x +5040 A a \right) x \left(d x \right)^{m}}{\left(m +7\right) \left(m +6\right) \left(m +5\right) \left(m +4\right) \left(m +3\right) \left(m +2\right) \left(m +1\right)}"," ",0,"x*(C*c*m^6*x^6+B*c*m^6*x^5+21*C*c*m^5*x^6+A*c*m^6*x^4+22*B*c*m^5*x^5+C*b*m^6*x^4+175*C*c*m^4*x^6+23*A*c*m^5*x^4+B*b*m^6*x^3+190*B*c*m^4*x^5+23*C*b*m^5*x^4+735*C*c*m^3*x^6+A*b*m^6*x^2+207*A*c*m^4*x^4+24*B*b*m^5*x^3+820*B*c*m^3*x^5+C*a*m^6*x^2+207*C*b*m^4*x^4+1624*C*c*m^2*x^6+25*A*b*m^5*x^2+925*A*c*m^3*x^4+B*a*m^6*x+226*B*b*m^4*x^3+1849*B*c*m^2*x^5+25*C*a*m^5*x^2+925*C*b*m^3*x^4+1764*C*c*m*x^6+A*a*m^6+247*A*b*m^4*x^2+2144*A*c*m^2*x^4+26*B*a*m^5*x+1056*B*b*m^3*x^3+2038*B*c*m*x^5+247*C*a*m^4*x^2+2144*C*b*m^2*x^4+720*C*c*x^6+27*A*a*m^5+1219*A*b*m^3*x^2+2412*A*c*m*x^4+270*B*a*m^4*x+2545*B*b*m^2*x^3+840*B*c*x^5+1219*C*a*m^3*x^2+2412*C*b*m*x^4+295*A*a*m^4+3112*A*b*m^2*x^2+1008*A*c*x^4+1420*B*a*m^3*x+2952*B*b*m*x^3+3112*C*a*m^2*x^2+1008*C*b*x^4+1665*A*a*m^3+3796*A*b*m*x^2+3929*B*a*m^2*x+1260*B*b*x^3+3796*C*a*m*x^2+5104*A*a*m^2+1680*A*b*x^2+5274*B*a*m*x+1680*C*a*x^2+8028*A*a*m+2520*B*a*x+5040*A*a)*(d*x)^m/(m+7)/(m+6)/(m+5)/(m+4)/(m+3)/(m+2)/(m+1)","B"
40,0,0,334,0.035000," ","int((d*x)^m*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x)","\int \frac{\left(C \,x^{2}+B x +A \right) \left(d x \right)^{m}}{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int((d*x)^m*(C*x^2+B*x+A)/(c*x^4+b*x^2+a),x)","F"
41,0,0,629,0.031000," ","int((d*x)^m*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x)","\int \frac{\left(C \,x^{2}+B x +A \right) \left(d x \right)^{m}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}\, dx"," ",0,"int((d*x)^m*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x)","F"
42,1,1119,306,0.000000," ","int(x^2*(C*x^2+B*x+A)/(c*x^4+b*x^2+a)^2,x)","-\frac{2 \sqrt{2}\, A a \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, A a \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, A \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C a b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C a b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}-\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}+\frac{-\frac{B b \,x^{2}}{2 \left(4 a c -b^{2}\right)}+\frac{\left(2 A c -b C \right) x^{3}}{8 a c -2 b^{2}}-\frac{B a}{4 a c -b^{2}}+\frac{\left(A b -2 a C \right) x}{8 a c -2 b^{2}}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2/(4*a*c-b^2)*B*b*x^2+1/2*(2*A*c-C*b)/(4*a*c-b^2)*x^3-1/(4*a*c-b^2)*B*a+1/2*(A*b-2*C*a)/(4*a*c-b^2)*x)/(c*x^4+b*x^2+a)+1/2/(4*a*c-b^2)^2*(-4*a*c+b^2)^(1/2)*B*b*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))-c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b-2*c^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A+1/2*c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*a+1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a*b-1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*C-1/2/(4*a*c-b^2)^2*(-4*a*c+b^2)^(1/2)*B*b*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))-1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*A*b*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*A*a*c^2*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*A*b^2*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*C*a*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*C*b^2*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*C*a*b*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*C*b^3*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)","B"
43,1,1119,306,0.036000," ","int(x*(C*x^3+B*x^2+A*x)/(c*x^4+b*x^2+a)^2,x)","-\frac{2 \sqrt{2}\, A a \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, A a \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, A \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C a b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C a b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}-\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}+\frac{-\frac{B b \,x^{2}}{2 \left(4 a c -b^{2}\right)}+\frac{\left(2 A c -b C \right) x^{3}}{8 a c -2 b^{2}}-\frac{B a}{4 a c -b^{2}}+\frac{\left(A b -2 a C \right) x}{8 a c -2 b^{2}}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2/(4*a*c-b^2)*B*b*x^2+1/2*(2*A*c-C*b)/(4*a*c-b^2)*x^3-1/(4*a*c-b^2)*B*a+1/2*(A*b-2*C*a)/(4*a*c-b^2)*x)/(c*x^4+b*x^2+a)+1/2/(4*a*c-b^2)^2*(-4*a*c+b^2)^(1/2)*B*b*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))-c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b-2*c^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A+1/2*c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*a+1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a*b-1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*C-1/2/(4*a*c-b^2)^2*(-4*a*c+b^2)^(1/2)*B*b*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))-1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*A*b*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*A*a*c^2*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*A*b^2*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*C*a*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*C*b^2*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*C*a*b*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*C*b^3*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)","B"
44,1,1119,306,0.039000," ","int((C*x^4+B*x^3+A*x^2)/(c*x^4+b*x^2+a)^2,x)","-\frac{2 \sqrt{2}\, A a \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, A a \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, A \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C a b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C a b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}-\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}+\frac{-\frac{B b \,x^{2}}{2 \left(4 a c -b^{2}\right)}+\frac{\left(2 A c -b C \right) x^{3}}{8 a c -2 b^{2}}-\frac{B a}{4 a c -b^{2}}+\frac{\left(A b -2 a C \right) x}{8 a c -2 b^{2}}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2/(4*a*c-b^2)*B*b*x^2+1/2*(2*A*c-C*b)/(4*a*c-b^2)*x^3-1/(4*a*c-b^2)*B*a+1/2*(A*b-2*C*a)/(4*a*c-b^2)*x)/(c*x^4+b*x^2+a)+1/2/(4*a*c-b^2)^2*(-4*a*c+b^2)^(1/2)*B*b*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))-c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b-2*c^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A+1/2*c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*a+1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a*b-1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*C-1/2/(4*a*c-b^2)^2*(-4*a*c+b^2)^(1/2)*B*b*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))-1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*A*b*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*A*a*c^2*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*A*b^2*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*C*a*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*C*b^2*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*C*a*b*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*C*b^3*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)","B"
45,1,1119,306,0.034000," ","int((C*x^5+B*x^4+A*x^3)/x/(c*x^4+b*x^2+a)^2,x)","-\frac{2 \sqrt{2}\, A a \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, A a \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, A \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C a b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C a b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}-\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}+\frac{-\frac{B b \,x^{2}}{2 \left(4 a c -b^{2}\right)}+\frac{\left(2 A c -b C \right) x^{3}}{8 a c -2 b^{2}}-\frac{B a}{4 a c -b^{2}}+\frac{\left(A b -2 a C \right) x}{8 a c -2 b^{2}}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2/(4*a*c-b^2)*B*b*x^2+1/2*(2*A*c-C*b)/(4*a*c-b^2)*x^3-1/(4*a*c-b^2)*B*a+1/2*(A*b-2*C*a)/(4*a*c-b^2)*x)/(c*x^4+b*x^2+a)+1/2/(4*a*c-b^2)^2*(-4*a*c+b^2)^(1/2)*B*b*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))-c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b-2*c^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A+1/2*c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*a+1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a*b-1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*C-1/2/(4*a*c-b^2)^2*(-4*a*c+b^2)^(1/2)*B*b*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))-1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*A*b*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*A*a*c^2*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*A*b^2*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*C*a*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*C*b^2*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*C*a*b*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*C*b^3*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)","B"
46,1,1119,306,0.033000," ","int((C*x^6+B*x^5+A*x^4)/x^2/(c*x^4+b*x^2+a)^2,x)","-\frac{2 \sqrt{2}\, A a \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, A a \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, A \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C a b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C a b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, C \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, C \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, A b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \sqrt{-4 a c +b^{2}}\, C \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right)^{2} \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(-2 c \,x^{2}-b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}-\frac{\sqrt{-4 a c +b^{2}}\, B b \ln \left(2 c \,x^{2}+b +\sqrt{-4 a c +b^{2}}\right)}{2 \left(4 a c -b^{2}\right)^{2}}+\frac{-\frac{B b \,x^{2}}{2 \left(4 a c -b^{2}\right)}+\frac{\left(2 A c -b C \right) x^{3}}{8 a c -2 b^{2}}-\frac{B a}{4 a c -b^{2}}+\frac{\left(A b -2 a C \right) x}{8 a c -2 b^{2}}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2/(4*a*c-b^2)*B*b*x^2+1/2*(2*A*c-C*b)/(4*a*c-b^2)*x^3-1/(4*a*c-b^2)*B*a+1/2*(A*b-2*C*a)/(4*a*c-b^2)*x)/(c*x^4+b*x^2+a)+1/2/(4*a*c-b^2)^2*(-4*a*c+b^2)^(1/2)*B*b*ln(-2*c*x^2-b+(-4*a*c+b^2)^(1/2))-c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*(-4*a*c+b^2)^(1/2)*b-2*c^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A+1/2*c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*a+1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*(-4*a*c+b^2)^(1/2)*b^2+c/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*C*a*b-1/4/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*C-1/2/(4*a*c-b^2)^2*(-4*a*c+b^2)^(1/2)*B*b*ln(2*c*x^2+b+(-4*a*c+b^2)^(1/2))-1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*A*b*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*A*a*c^2*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*A*b^2*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*C*a*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*(-4*a*c+b^2)^(1/2)*C*b^2*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*C*a*b*c*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*C*b^3*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)","B"
47,1,622,257,0.007000," ","int(x^7*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{f \,x^{8}}{8 c}-\frac{b f \,x^{6}}{6 c^{2}}+\frac{e \,x^{6}}{6 c}-\frac{a f \,x^{4}}{4 c^{2}}+\frac{b^{2} f \,x^{4}}{4 c^{3}}-\frac{b e \,x^{4}}{4 c^{2}}+\frac{d \,x^{4}}{4 c}-\frac{5 a^{2} b f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{3}}+\frac{a^{2} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{2}}+\frac{5 a \,b^{3} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{4}}-\frac{2 a \,b^{2} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{3}}+\frac{3 a b d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{2}}+\frac{a b f \,x^{2}}{c^{3}}-\frac{a e \,x^{2}}{2 c^{2}}-\frac{b^{5} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{5}}+\frac{b^{4} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{4}}-\frac{b^{3} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{3}}-\frac{b^{3} f \,x^{2}}{2 c^{4}}+\frac{b^{2} e \,x^{2}}{2 c^{3}}-\frac{b d \,x^{2}}{2 c^{2}}+\frac{a^{2} f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{3}}-\frac{3 a \,b^{2} f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{4}}+\frac{a b e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 c^{3}}-\frac{a d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}+\frac{b^{4} f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{5}}-\frac{b^{3} e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{4}}+\frac{b^{2} d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{3}}"," ",0,"1/c^3*x^2*a*b*f+1/2/c^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^4*e+1/8*f*x^8/c-1/2/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*d+1/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^2*e-1/2/c^5/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^5*f-3/4/c^4*ln(c*x^4+b*x^2+a)*a*b^2*f+1/2/c^3*ln(c*x^4+b*x^2+a)*a*b*e+1/6/c*x^6*e+1/4/c*x^4*d+3/2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b*d+5/2/c^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b^3*f-2/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b^2*e-5/2/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^2*b*f-1/2/c^2*x^2*a*e-1/6/c^2*x^6*b*f-1/4/c^2*x^4*a*f-1/2/c^4*x^2*b^3*f+1/2/c^3*x^2*b^2*e-1/2/c^2*x^2*b*d+1/4/c^3*x^4*b^2*f-1/4/c^2*x^4*b*e+1/4/c^3*ln(c*x^4+b*x^2+a)*b^2*d+1/4/c^3*ln(c*x^4+b*x^2+a)*a^2*f-1/4/c^2*ln(c*x^4+b*x^2+a)*a*d+1/4/c^5*ln(c*x^4+b*x^2+a)*b^4*f-1/4/c^4*ln(c*x^4+b*x^2+a)*b^3*e","B"
48,1,474,189,0.006000," ","int(x^5*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{f \,x^{6}}{6 c}-\frac{b f \,x^{4}}{4 c^{2}}+\frac{e \,x^{4}}{4 c}+\frac{a^{2} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{2}}-\frac{2 a \,b^{2} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{3}}+\frac{3 a b e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{a d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}-\frac{a f \,x^{2}}{2 c^{2}}+\frac{b^{4} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{4}}-\frac{b^{3} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{3}}+\frac{b^{2} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{2}}+\frac{b^{2} f \,x^{2}}{2 c^{3}}-\frac{b e \,x^{2}}{2 c^{2}}+\frac{d \,x^{2}}{2 c}+\frac{a b f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 c^{3}}-\frac{a e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}-\frac{b^{3} f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{4}}+\frac{b^{2} e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{3}}-\frac{b d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}"," ",0,"1/6*f*x^6/c-1/4/c^2*x^4*b*f+1/4/c*x^4*e-1/2/c^2*x^2*a*f+1/2/c^3*x^2*b^2*f-1/2/c^2*x^2*b*e+1/2/c*x^2*d+1/2/c^3*ln(c*x^4+b*x^2+a)*a*b*f-1/4/c^2*ln(c*x^4+b*x^2+a)*a*e-1/4/c^4*ln(c*x^4+b*x^2+a)*b^3*f+1/4/c^3*ln(c*x^4+b*x^2+a)*b^2*e-1/4/c^2*ln(c*x^4+b*x^2+a)*b*d+1/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^2*f-2/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b^2*f+3/2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b*e-1/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*d+1/2/c^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^4*f-1/2/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*e+1/2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*d","B"
49,1,321,132,0.006000," ","int(x^3*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{f \,x^{4}}{4 c}+\frac{3 a b f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{a e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}-\frac{b^{3} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{3}}+\frac{b^{2} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{b d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c}-\frac{b f \,x^{2}}{2 c^{2}}+\frac{e \,x^{2}}{2 c}-\frac{a f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}+\frac{b^{2} f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{3}}-\frac{b e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}+\frac{d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c}"," ",0,"1/4*f*x^4/c-1/2/c^2*x^2*b*f+1/2/c*x^2*e-1/4/c^2*ln(c*x^4+b*x^2+a)*a*f+1/4/c^3*ln(c*x^4+b*x^2+a)*b^2*f-1/4/c^2*ln(c*x^4+b*x^2+a)*b*e+1/4/c*ln(c*x^4+b*x^2+a)*d+3/2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b*f-1/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*e-1/2/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*f+1/2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*e-1/2/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*d","B"
50,1,211,93,0.004000," ","int(x*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x)","-\frac{a f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{b^{2} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{b e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c}+\frac{f \,x^{2}}{2 c}+\frac{d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{b f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}+\frac{e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c}"," ",0,"1/2*f*x^2/c-1/4/c^2*ln(c*x^4+b*x^2+a)*b*f+1/4/c*ln(c*x^4+b*x^2+a)*e-1/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*f+1/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*d+1/2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*f-1/2/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*e","B"
51,1,165,89,0.009000," ","int((f*x^4+e*x^2+d)/x/(c*x^4+b*x^2+a),x)","-\frac{b d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a}-\frac{b f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c}+\frac{e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+\frac{d \ln \left(x \right)}{a}-\frac{d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a}+\frac{f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c}"," ",0,"d*ln(x)/a+1/4/c*ln(c*x^4+b*x^2+a)*f-1/4/a*ln(c*x^4+b*x^2+a)*d+1/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*e-1/2/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*d-1/2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b/c*f","A"
52,1,227,108,0.010000," ","int((f*x^4+e*x^2+d)/x^3/(c*x^4+b*x^2+a),x)","-\frac{b e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a}-\frac{c d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a}+\frac{b^{2} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a^{2}}+\frac{f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+\frac{e \ln \left(x \right)}{a}-\frac{e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a}-\frac{b d \ln \left(x \right)}{a^{2}}+\frac{b d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a^{2}}-\frac{d}{2 a \,x^{2}}"," ",0,"-1/2*d/a/x^2+1/a*ln(x)*e-1/a^2*ln(x)*b*d-1/4/a*ln(c*x^4+b*x^2+a)*e+1/4/a^2*ln(c*x^4+b*x^2+a)*b*d+1/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*f-1/2/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*e-1/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c*d+1/2/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*d","B"
53,1,356,162,0.012000," ","int((f*x^4+e*x^2+d)/x^5/(c*x^4+b*x^2+a),x)","-\frac{b f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a}-\frac{c e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a}+\frac{b^{2} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a^{2}}+\frac{3 b c d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a^{2}}-\frac{b^{3} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a^{3}}+\frac{f \ln \left(x \right)}{a}-\frac{f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a}-\frac{b e \ln \left(x \right)}{a^{2}}+\frac{b e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a^{2}}-\frac{c d \ln \left(x \right)}{a^{2}}+\frac{c d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a^{2}}+\frac{b^{2} d \ln \left(x \right)}{a^{3}}-\frac{b^{2} d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a^{3}}-\frac{e}{2 a \,x^{2}}+\frac{b d}{2 a^{2} x^{2}}-\frac{d}{4 a \,x^{4}}"," ",0,"-1/4*d/a/x^4-1/2/a/x^2*e+1/2/a^2/x^2*b*d+1/a*ln(x)*f-1/a^2*ln(x)*b*e-1/a^2*ln(x)*c*d+1/a^3*ln(x)*b^2*d-1/4/a*ln(c*x^4+b*x^2+a)*f+1/4/a^2*ln(c*x^4+b*x^2+a)*b*e+1/4/a^2*c*ln(c*x^4+b*x^2+a)*d-1/4/a^3*ln(c*x^4+b*x^2+a)*b^2*d-1/2/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*f-1/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c*e+1/2/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*e+3/2/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*c*d-1/2/a^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*d","B"
54,1,523,229,0.013000," ","int((f*x^4+e*x^2+d)/x^7/(c*x^4+b*x^2+a),x)","-\frac{c f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a}+\frac{b^{2} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a^{2}}+\frac{3 b c e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a^{2}}+\frac{c^{2} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{2}}-\frac{b^{3} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a^{3}}-\frac{2 b^{2} c d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{3}}+\frac{b^{4} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a^{4}}-\frac{b f \ln \left(x \right)}{a^{2}}+\frac{b f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a^{2}}-\frac{c e \ln \left(x \right)}{a^{2}}+\frac{c e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a^{2}}+\frac{b^{2} e \ln \left(x \right)}{a^{3}}-\frac{b^{2} e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a^{3}}+\frac{2 b c d \ln \left(x \right)}{a^{3}}-\frac{b c d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 a^{3}}-\frac{b^{3} d \ln \left(x \right)}{a^{4}}+\frac{b^{3} d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a^{4}}-\frac{f}{2 a \,x^{2}}+\frac{b e}{2 a^{2} x^{2}}+\frac{c d}{2 a^{2} x^{2}}-\frac{b^{2} d}{2 a^{3} x^{2}}-\frac{e}{4 a \,x^{4}}+\frac{b d}{4 a^{2} x^{4}}-\frac{d}{6 a \,x^{6}}"," ",0,"-1/6*d/a/x^6-1/4/a/x^4*e+1/4/a^2/x^4*b*d-1/2/a/x^2*f+1/2/a^2/x^2*b*e+1/2/a^2/x^2*c*d-1/2/a^3/x^2*b^2*d-1/a^2*ln(x)*b*f-1/a^2*ln(x)*c*e+1/a^3*ln(x)*b^2*e+2/a^3*ln(x)*b*c*d-1/a^4*ln(x)*b^3*d+1/4/a^2*ln(c*x^4+b*x^2+a)*b*f+1/4/a^2*c*ln(c*x^4+b*x^2+a)*e-1/4/a^3*ln(c*x^4+b*x^2+a)*b^2*e-1/2/a^3*c*ln(c*x^4+b*x^2+a)*b*d+1/4/a^4*ln(c*x^4+b*x^2+a)*b^3*d-1/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c*f+1/2/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*f+3/2/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*c*e+1/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c^2*d-1/2/a^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*e-2/a^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*c*d+1/2/a^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^4*d","B"
55,1,1450,329,0.035000," ","int(x^4*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{f \,x^{5}}{5 c}-\frac{\sqrt{2}\, a^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{2 \sqrt{2}\, a \,b^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{2 \sqrt{2}\, a \,b^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{3 \sqrt{2}\, a b e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, a b e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, a d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{4} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{3}}-\frac{\sqrt{2}\, b^{4} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{3}}+\frac{\sqrt{2}\, b^{3} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{3} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, b^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{b f \,x^{3}}{3 c^{2}}+\frac{e \,x^{3}}{3 c}-\frac{\sqrt{2}\, a b f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, a b f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, a e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b^{3} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{3}}-\frac{\sqrt{2}\, b^{3} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{3}}-\frac{\sqrt{2}\, b^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{a f x}{c^{2}}+\frac{b^{2} f x}{c^{3}}-\frac{b e x}{c^{2}}+\frac{d x}{c}"," ",0,"1/5*f*x^5/c-1/3/c^2*x^3*b*f-1/c^2*a*f*x+1/c^3*b^2*f*x-1/c^2*b*e*x-1/c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*f-1/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*f-1/2/c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*f+1/2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e-1/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+1/c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*f-1/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*f-1/2/c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*f+1/2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e-1/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d-1/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d+1/3/c*x^3*e+1/c*d*x+1/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e+1/2/c^3*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*f-1/2/c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+1/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d-1/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e-1/2/c^3*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*f+1/2/c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*f-3/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*e+2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*f-3/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*e","B"
56,1,1035,244,0.030000," ","int(x^2*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x)","-\frac{3 \sqrt{2}\, a b f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, a b f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, a e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b^{3} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{3} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, b^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{f \,x^{3}}{3 c}+\frac{\sqrt{2}\, a f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{b f x}{c^{2}}+\frac{e x}{c}"," ",0,"1/3*f*x^3/c-1/c^2*b*f*x+1/c*e*x+1/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*f-1/2/c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f+1/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-1/2*d*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-3/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*f+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e+1/2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*f-1/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-1/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*f+1/2/c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f-1/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e+1/2*d*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-3/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*f+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e+1/2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*f-1/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d","B"
57,1,676,184,0.027000," ","int((f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, a f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{f x}{c}"," ",0,"f*x/c+1/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f-1/2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*f-1/2/(-4*a*c+b^2)^(1/2)/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f+1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-1/(-4*a*c+b^2)^(1/2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d-1/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f+1/2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*f-1/2/(-4*a*c+b^2)^(1/2)/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f+1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-1/(-4*a*c+b^2)^(1/2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d","B"
58,1,563,178,0.025000," ","int((f*x^4+e*x^2+d)/x^2/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, b c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{d}{a x}"," ",0,"-d/a/x-1/2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f+1/2/a*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+1/2/a*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+1/2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f-1/2/a*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+1/2/a*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d","B"
59,1,727,226,0.027000," ","int((f*x^4+e*x^2+d)/x^4/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, b c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b^{2} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, b^{2} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, c f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{e}{a x}+\frac{b d}{a^{2} x}-\frac{d}{3 a \,x^{3}}"," ",0,"-1/3*d/a/x^3-1/a/x*e+1/a^2/x*b*d+1/2/a*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e-1/2/a^2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f+1/2/a*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e+1/a*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d-1/2/a^2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d-1/2/a*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+1/2/a^2*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f+1/2/a*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e+1/a*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d-1/2/a^2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d","B"
60,1,1121,285,0.033000," ","int((f*x^4+e*x^2+d)/x^6/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, b c f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b c f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, c^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, c^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b^{2} c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, b^{2} c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, b \,c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b^{3} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}+\frac{\sqrt{2}\, b^{3} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}+\frac{\sqrt{2}\, c f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, c f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b^{2} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}-\frac{\sqrt{2}\, b^{2} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}-\frac{f}{a x}+\frac{b e}{a^{2} x}+\frac{c d}{a^{2} x}-\frac{b^{2} d}{a^{3} x}-\frac{e}{3 a \,x^{3}}+\frac{b d}{3 a^{2} x^{3}}-\frac{d}{5 a \,x^{5}}"," ",0,"-1/5*d/a/x^5+1/3/a^2/x^3*b*d+1/a^2/x*b*e+1/a^2/x*c*d-1/a^3/x*b^2*d+1/2/a^3*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+1/a*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+1/2/a^2*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-1/2/a^3*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+1/a*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e-1/2/a^2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-1/3/a/x^3*e-1/a/x*f+1/2/a*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f+1/2/a^3*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d-3/2/a^2*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-1/2/a*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f+1/2/a^2*c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+1/2/a*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f-1/2/a^2*c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d-3/2/a^2*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+1/2/a^3*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d-1/2/a^2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e-1/2/a^2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+1/2/a*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f","B"
61,1,1167,306,0.024000," ","int(x^7*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","-\frac{5 a^{2} b f \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{a^{2} e \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}+\frac{5 a \,b^{3} f \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{2 a \,b^{2} e \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{3 a b d \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{b^{5} f \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{4}}+\frac{b^{4} e \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{b^{3} d \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{15 a^{2} b f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}-\frac{6 a^{2} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}-\frac{10 a \,b^{3} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{3}}+\frac{6 a \,b^{2} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}-\frac{3 a b d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}+\frac{3 b^{5} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{4}}-\frac{b^{4} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{3}}+\frac{b^{3} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}+\frac{f \,x^{4}}{4 c^{2}}-\frac{a^{3} f}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{2 a^{2} b^{2} f}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{3 a^{2} b e}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{a^{2} d}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{2 a^{2} f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) c^{2}}-\frac{a \,b^{4} f}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{4}}+\frac{a \,b^{3} e}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{a \,b^{2} d}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{7 a \,b^{2} f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(4 a c -b^{2}\right) c^{3}}-\frac{2 a b e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) c^{2}}+\frac{a d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) c}-\frac{3 b^{4} f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) c^{4}}+\frac{b^{3} e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(4 a c -b^{2}\right) c^{3}}-\frac{b^{2} d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) c^{2}}-\frac{b f \,x^{2}}{c^{3}}+\frac{e \,x^{2}}{2 c^{2}}"," ",0,"-2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a*b^2*e+3/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a*b*d+5/2/c^3/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a*b^3*f-5/2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a^2*b*f-1/c^3*x^2*b*f-1/c^2/(c*x^4+b*x^2+a)*a^3/(4*a*c-b^2)*f+1/c/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*d+15/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^2*b*f-10/c^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b^3*f+6/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b^2*e-3/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b*d+7/2/c^3/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*a*b^2*f-2/c^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*a*b*e-1/2/c^4/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*b^5*f-1/2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*b^3*d-3/2/c^2/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*b*e-1/2/c^4/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*b^4*f-1/2/c^2/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*b^2*d+1/2/c^3/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*b^4*e+2/c^3/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*b^2*f+1/4/c^2*x^4*f+1/2/c^2*x^2*e+1/2/c^3/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*b^3*e+1/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a^2*e-1/c^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^4*e+1/2/c^3/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^3*e-2/c^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*a^2*f+1/c/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*a*d-3/4/c^4/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^4*f-1/4/c^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^2*d-6/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^2*e+3/2/c^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^5*f+1/2/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*d","B"
62,1,832,224,0.017000," ","int(x^5*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","\frac{a^{2} f \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{2 a \,b^{2} f \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{3 a b e \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{a d \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{b^{4} f \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{b^{3} e \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{b^{2} d \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{6 a^{2} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}+\frac{6 a \,b^{2} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}-\frac{3 a b e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}+\frac{2 a d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{b^{4} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{3}}+\frac{b^{3} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}-\frac{3 a^{2} b f}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{a^{2} e}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}+\frac{a \,b^{3} f}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{a \,b^{2} e}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{a b d}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{2 a b f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) c^{2}}+\frac{a e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) c}+\frac{b^{3} f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(4 a c -b^{2}\right) c^{3}}-\frac{b^{2} e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) c^{2}}+\frac{f \,x^{2}}{2 c^{2}}"," ",0,"1/2*f*x^2/c^2+1/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a^2*f-2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a*b^2*f+3/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a*b*e-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a*d+1/2/c^3/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*b^4*f-1/2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*b^3*e+1/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*b^2*d-3/2/c^2/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*b*f+1/c/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*e+1/2/c^3/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*b^3*f-1/2/c^2/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*b^2*e+1/2/c/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*b*d-2/c^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*a*b*f+1/c/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*a*e+1/2/c^3/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^3*f-1/4/c^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^2*e-6/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^2*f+6/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b^2*f-3/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b*e+2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*d-1/c^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^4*f+1/2/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*e","B"
63,1,336,155,0.015000," ","int(x^3*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","-\frac{3 a b f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}+\frac{2 a e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{b^{3} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}-\frac{b d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{a f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) c}-\frac{b^{2} f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) c^{2}}+\frac{\frac{\left(3 a b c f -2 a \,c^{2} e -b^{3} f +b^{2} c e -b \,c^{2} d \right) x^{2}}{\left(4 a c -b^{2}\right) c^{2}}+\frac{\left(2 a c f -b^{2} f +b c e -2 c^{2} d \right) a}{\left(4 a c -b^{2}\right) c^{2}}}{2 c \,x^{4}+2 b \,x^{2}+2 a}"," ",0,"1/2*((3*a*b*c*f-2*a*c^2*e-b^3*f+b^2*c*e-b*c^2*d)/(4*a*c-b^2)/c^2*x^2+a*(2*a*c*f-b^2*f+b*c*e-2*c^2*d)/(4*a*c-b^2)/c^2)/(c*x^4+b*x^2+a)+1/c/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*a*f-1/4/c^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^2*f-3/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b*f+2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*e-1/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*d+1/2/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*f","B"
64,1,205,117,0.012000," ","int(x*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","\frac{2 a f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{b e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 c d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{-\frac{\left(2 a c f -b^{2} f +b c e -2 c^{2} d \right) x^{2}}{\left(4 a c -b^{2}\right) c}+\frac{a b f -2 a c e +b c d}{\left(4 a c -b^{2}\right) c}}{2 c \,x^{4}+2 b \,x^{2}+2 a}"," ",0,"1/2*(-(2*a*c*f-b^2*f+b*c*e-2*c^2*d)/(4*a*c-b^2)/c*x^2+1/c*(a*b*f-2*a*c*e+b*c*d)/(4*a*c-b^2))/(c*x^4+b*x^2+a)+2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*f-1/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*e+2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c*d","A"
65,1,462,156,0.017000," ","int((f*x^4+e*x^2+d)/x/(c*x^4+b*x^2+a)^2,x)","-\frac{b c d \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{b f \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{c e \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{3 b c d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a}+\frac{b^{3} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}-\frac{b f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 c e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{a f}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{b^{2} d}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{c d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a}+\frac{b^{2} d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) a^{2}}+\frac{b e}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{c d}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{d \ln \left(x \right)}{a^{2}}"," ",0,"d*ln(x)/a^2-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*b*f+c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*e-1/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*b*c*d-a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*f+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b*e+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*c*d-1/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^2*d-1/a/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)*d+1/4/a^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^2*d-1/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*f+2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c*e-3/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*c*d+1/2/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*d","B"
66,1,722,222,0.023000," ","int((f*x^4+e*x^2+d)/x^3/(c*x^4+b*x^2+a)^2,x)","-\frac{b c e \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{c^{2} d \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{2} c d \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{c f \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{3 b c e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a}-\frac{6 c^{2} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a}+\frac{b^{3} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}+\frac{6 b^{2} c d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}-\frac{b^{4} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{3}}+\frac{2 c f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}-\frac{b^{2} e}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{3 b c d}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{c e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a}+\frac{b^{3} d}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{b^{2} e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) a^{2}}+\frac{2 b c d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a^{2}}-\frac{b^{3} d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(4 a c -b^{2}\right) a^{3}}+\frac{b f}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{c e}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{e \ln \left(x \right)}{a^{2}}-\frac{2 b d \ln \left(x \right)}{a^{3}}-\frac{d}{2 a^{2} x^{2}}"," ",0,"-1/2*d/a^2/x^2+1/a^2*ln(x)*e-2/a^3*ln(x)*b*d+1/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*f-1/2/a/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*b*e-1/a/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^2*d+1/2/a^2/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*b^2*d+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b*f+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*c*e-1/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^2*e-3/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b*c*d+1/2/a^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^3*d-1/a/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)*e+1/4/a^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^2*e+2/a^2/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)*b*d-1/2/a^3/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^3*d+2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c*f-3/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*c*e-6/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c^2*d+1/2/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*e+6/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*c*d-1/a^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^4*d","B"
67,1,1078,315,0.029000," ","int((f*x^4+e*x^2+d)/x^5/(c*x^4+b*x^2+a)^2,x)","-\frac{b c f \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{c^{2} e \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{2} c e \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{3 b \,c^{2} d \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{b^{3} c d \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{3}}-\frac{3 b c f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a}-\frac{6 c^{2} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a}+\frac{b^{3} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}+\frac{6 b^{2} c e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}+\frac{15 b \,c^{2} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}-\frac{b^{4} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{3}}-\frac{10 b^{3} c d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{3}}+\frac{3 b^{5} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{4}}-\frac{b^{2} f}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{3 b c e}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{c^{2} d}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{c f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a}+\frac{b^{3} e}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{2 b^{2} c d}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{b^{2} f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) a^{2}}+\frac{2 b c e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a^{2}}+\frac{2 c^{2} d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a^{2}}-\frac{b^{4} d}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{3}}-\frac{b^{3} e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(4 a c -b^{2}\right) a^{3}}-\frac{7 b^{2} c d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(4 a c -b^{2}\right) a^{3}}+\frac{3 b^{4} d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) a^{4}}+\frac{c f}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{f \ln \left(x \right)}{a^{2}}-\frac{2 b e \ln \left(x \right)}{a^{3}}-\frac{2 c d \ln \left(x \right)}{a^{3}}+\frac{3 b^{2} d \ln \left(x \right)}{a^{4}}-\frac{e}{2 a^{2} x^{2}}+\frac{b d}{a^{3} x^{2}}-\frac{d}{4 a^{2} x^{4}}"," ",0,"-1/4*d/a^2/x^4+1/a^3/x^2*b*d-2/a^3*ln(x)*b*e-2/a^3*ln(x)*c*d+3/a^4*ln(x)*b^2*d+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*c*f+6/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*c*e+15/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*c^2*d-10/a^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*c*d-1/a/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^2*e-3/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b*c*e+2/a^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^2*c*d+2/a^2/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)*b*e-7/2/a^3/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)*b^2*d-3/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*c*f-1/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^2*f-1/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*c^2*d-1/2/a/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*b*f+1/2/a^2/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*b^2*e+3/2/a^2/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^2*b*d-1/2/a^3/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*b^3*d-1/2/a^2/x^2*e+1/a^2*ln(x)*f+1/2/a^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^3*e-1/2/a^3/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^4*d+3/4/a^4/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^4*d+3/2/a^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^5*d-6/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c^2*e+1/2/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*f-1/a^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^4*e-1/a/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)*f+1/4/a^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^2*f+2/a^2/(4*a*c-b^2)*c^2*ln(c*x^4+b*x^2+a)*d-1/2/a^3/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^3*e","B"
68,1,2558,504,0.056000," ","int(x^6*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","\frac{a^{2} f \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{2 a \,b^{2} f \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{3 a b e \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{a d \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{b^{4} f \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{b^{3} e \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{b^{2} d \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{13 \sqrt{2}\, a^{2} b f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{13 \sqrt{2}\, a^{2} b f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{5 \sqrt{2}\, a^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{5 \sqrt{2}\, a^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{17 \sqrt{2}\, a \,b^{3} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{17 \sqrt{2}\, a \,b^{3} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{19 \sqrt{2}\, a \,b^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{19 \sqrt{2}\, a \,b^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{2 \sqrt{2}\, a b d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{5 \sqrt{2}\, b^{5} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{3}}-\frac{5 \sqrt{2}\, b^{5} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{3}}+\frac{3 \sqrt{2}\, b^{4} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b^{4} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, b^{3} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{3} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 a^{2} b f x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{a^{2} e x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}+\frac{7 \sqrt{2}\, a^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{7 \sqrt{2}\, a^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{a \,b^{3} f x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{a \,b^{2} e x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}-\frac{6 \sqrt{2}\, a \,b^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{6 \sqrt{2}\, a \,b^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{a b d x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}+\frac{13 \sqrt{2}\, a b e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{13 \sqrt{2}\, a b e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, a d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{5 \sqrt{2}\, b^{4} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{3}}-\frac{5 \sqrt{2}\, b^{4} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{3}}-\frac{3 \sqrt{2}\, b^{3} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b^{3} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{f \,x^{3}}{3 c^{2}}-\frac{2 b f x}{c^{3}}+\frac{e x}{c^{2}}"," ",0,"1/3*f*x^3/c^2-2/c^3*b*f*x+1/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a^2*f-1/2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b^3*e+1/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b^2*d+1/c/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*x*e+1/2/c^3/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b^4*f+3/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d-3/2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d+13/4/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*e+6/c^2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*f-6/c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*f-1/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d-13/4/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*e+2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*d+2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*d-5/4/c^3/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^5*f+3/4/c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*e-1/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d-5/4/c^3/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^5*f+3/4/c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*e-19/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*e+17/2/c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^3*f-13/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*b*f+17/2/c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^3*f-19/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*e-13/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*b*f+1/c^2*e*x-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a*d+1/2/c^3/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*b^3*f-2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a*b^2*f+3/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a*b*e-3/2/c^2/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*x*b*f-1/2/c^2/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*b^2*e+1/2/c/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*b*d+5/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*e+5/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*e-3/4/c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e+1/4/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d-7/2/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*f-5/4/c^3/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*f+3/4/c^2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e-1/4/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+7/2/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*f+5/4/c^3/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*f","B"
69,1,1977,395,0.052000," ","int(x^4*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","\frac{3 a b f \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{a e \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{b^{3} f \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{b^{2} e \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{b d \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{5 \sqrt{2}\, a^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{5 \sqrt{2}\, a^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{19 \sqrt{2}\, a \,b^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{19 \sqrt{2}\, a \,b^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{2 \sqrt{2}\, a b e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, a b e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, b^{4} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b^{4} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, b^{3} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{3} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{a^{2} f x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{a \,b^{2} f x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{a b e x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}+\frac{13 \sqrt{2}\, a b f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{13 \sqrt{2}\, a b f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{a d x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{3 \sqrt{2}\, a e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, a e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, b^{3} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b^{3} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{f x}{c^{2}}"," ",0,"-1/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e+13/4/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*f-13/4/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*f+f*x/c^2+1/2/c/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*b*e+3/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a*b*f-1/2/c^2/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*b^2*f-3/4/c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*f+1/4/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+3/4/c^2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*f-1/4/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+5/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*f+3/4/c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*f-1/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e+2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*e-1/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*d-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a*e-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b*d-c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d+3/4/c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*f+2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*e-c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d-19/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*f-19/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*f-1/2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b^3*f+1/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b^2*e+1/c/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*x*f-3/2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e+1/4/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+3/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+5/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*f","B"
70,1,1300,321,0.043000," ","int(x^2*(f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","\frac{2 \sqrt{2}\, a b f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, a b f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{3} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{3} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, a f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, a f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{-\frac{\left(2 a c f -b^{2} f +b c e -2 c^{2} d \right) x^{3}}{2 \left(4 a c -b^{2}\right) c}+\frac{\left(a b f -2 a c e +b c d \right) x}{2 \left(4 a c -b^{2}\right) c}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2*(2*a*c*f-b^2*f+b*c*e-2*c^2*d)/(4*a*c-b^2)/c*x^3+1/2*(a*b*f-2*a*c*e+b*c*d)/(4*a*c-b^2)/c*x)/(c*x^4+b*x^2+a)-3/2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*f+1/4/(4*a*c-b^2)/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f+1/4/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-1/2/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*f-1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e-1/4/(4*a*c-b^2)/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*f-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+3/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*f-1/4/(4*a*c-b^2)/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e+1/2/(4*a*c-b^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*f-1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e-1/4/(4*a*c-b^2)/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*f-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d","B"
71,1,1182,304,0.040000," ","int((f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","-\frac{\sqrt{2}\, a c f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a c f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b^{2} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{-\frac{\left(a b f -2 a c e +b c d \right) x^{3}}{2 \left(4 a c -b^{2}\right) a}-\frac{\left(2 f \,a^{2}-a b e -2 a c d +b^{2} d \right) x}{2 \left(4 a c -b^{2}\right) a}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2/a*(a*b*f-2*a*c*e+b*c*d)/(4*a*c-b^2)*x^3-1/2*(2*a^2*f-a*b*e-2*a*c*d+b^2*d)/a/(4*a*c-b^2)*x)/(c*x^4+b*x^2+a)+1/4/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f-1/2/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+1/4/a/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f+1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-3/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+1/4/a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f+1/2/(4*a*c-b^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e-1/4/a/(4*a*c-b^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f+1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-3/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+1/4/a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d","B"
72,1,1575,355,0.048000," ","int((f*x^4+e*x^2+d)/x^2/(c*x^4+b*x^2+a)^2,x)","-\frac{b c e \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{c^{2} d \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{2} c d \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{c f \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{\sqrt{2}\, b^{2} c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, b \,c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \sqrt{2}\, b^{3} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, b^{3} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b c f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{b^{2} e x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{3 b c d x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{\sqrt{2}\, b c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{5 \sqrt{2}\, c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{5 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{b^{3} d x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{3 \sqrt{2}\, b^{2} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{3 \sqrt{2}\, b^{2} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{b f x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{c e x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{\sqrt{2}\, c f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{d}{a^{2} x}"," ",0,"4/a*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+4/a*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-3/4/a^2*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d-3/4/a^2*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d+1/4/a*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+1/4/a*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e-d/a^2/x+1/4/a*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-1/a/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^3*d-1/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b^2*e+1/2/a^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b^3*d-1/2*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f+1/2*c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f-1/4/a*c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e+c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f+c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f-3/4/a^2*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+3/4/a^2*c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*c*e+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b*f+c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*f+1/2/a^2/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*b^2*d+5/2/a*c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d-5/2/a*c^2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d-3*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e-3*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e-1/2/a/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*b*e-3/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b*c*d","B"
73,1,2180,511,0.065000," ","int((f*x^4+e*x^2+d)/x^4/(c*x^4+b*x^2+a)^2,x)","-\frac{b c f \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{c^{2} e \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{2} c e \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{3 b \,c^{2} d \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{b^{3} c d \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{3}}+\frac{\sqrt{2}\, b^{2} c f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} c f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, b \,c^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, b \,c^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{7 \sqrt{2}\, c^{3} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{7 \sqrt{2}\, c^{3} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \sqrt{2}\, b^{3} c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, b^{3} c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{29 \sqrt{2}\, b^{2} c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{29 \sqrt{2}\, b^{2} c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{5 \sqrt{2}\, b^{4} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}+\frac{5 \sqrt{2}\, b^{4} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}-\frac{3 \sqrt{2}\, c^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{b^{2} f x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{3 b c e x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{\sqrt{2}\, b c f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{c^{2} d x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{5 \sqrt{2}\, c^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{5 \sqrt{2}\, c^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{b^{3} e x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{2 b^{2} c d x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{3 \sqrt{2}\, b^{2} c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{3 \sqrt{2}\, b^{2} c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{19 \sqrt{2}\, b \,c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{19 \sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{b^{4} d x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{3}}+\frac{5 \sqrt{2}\, b^{3} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}-\frac{5 \sqrt{2}\, b^{3} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}+\frac{c f x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{e}{a^{2} x}+\frac{2 b d}{a^{3} x}-\frac{d}{3 a^{2} x^{3}}"," ",0,"-1/3*d/a^2/x^3+2/a^3/x*b*d-5/4/a^3*c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d+7/a*c^3/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+1/4/a*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f-3/4/a^2*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e-1/4/a*c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f+3/4/a^2*c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+19/4/a^2*c^2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+7/a*c^3/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d-19/4/a^2*c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+5/4/a^3*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d-29/4/a^2*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+1/4/a*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f+4/a*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-3/4/a^2*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e+4/a*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-3/4/a^2*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e+1/4/a*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f+5/4/a^3*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*d+5/4/a^3*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*d-29/4/a^2*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d-1/2/a/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*b*f+1/2/a^2/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*b^2*e+3/2/a^2/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^3*b*d-3/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b*c*e+2/a^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b^2*c*d-1/2/a^3/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*b^3*d+5/2/a*c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e-5/2/a*c^2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e-3*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f-3*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*c*f-1/a/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^3*e-1/2/a^3/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b^4*d-1/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b^2*f-1/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*c^2*d+1/2/a^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b^3*e-1/a^2/x*e","B"
74,1,56,58,0.017000," ","int(x^9*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x)","\frac{5 x^{8}}{8}-\frac{9 x^{6}}{2}+\frac{49 x^{4}}{2}-\frac{293 x^{2}}{2}+2 \ln \left(x^{2}+1\right)+392 \ln \left(x^{2}+2\right)-\frac{1}{2 \left(x^{2}+1\right)}+\frac{208}{x^{2}+2}"," ",0,"5/8*x^8-9/2*x^6+49/2*x^4-293/2*x^2+2*ln(x^2+1)-1/2/(x^2+1)+208/(x^2+2)+392*ln(x^2+2)","A"
75,1,51,53,0.016000," ","int(x^7*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x)","\frac{5 x^{6}}{6}-\frac{27 x^{4}}{4}+49 x^{2}-\frac{5 \ln \left(x^{2}+1\right)}{2}-144 \ln \left(x^{2}+2\right)+\frac{1}{2 x^{2}+2}-\frac{104}{x^{2}+2}"," ",0,"5/6*x^6-27/4*x^4+49*x^2-5/2*ln(x^2+1)+1/2/(x^2+1)-104/(x^2+2)-144*ln(x^2+2)","A"
76,1,46,48,0.016000," ","int(x^5*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x)","\frac{5 x^{4}}{4}-\frac{27 x^{2}}{2}+3 \ln \left(x^{2}+1\right)+46 \ln \left(x^{2}+2\right)-\frac{1}{2 \left(x^{2}+1\right)}+\frac{52}{x^{2}+2}"," ",0,"5/4*x^4-27/2*x^2+3*ln(x^2+1)-1/2/(x^2+1)+52/(x^2+2)+46*ln(x^2+2)","A"
77,1,41,43,0.015000," ","int(x^3*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x)","\frac{5 x^{2}}{2}-\frac{7 \ln \left(x^{2}+1\right)}{2}-10 \ln \left(x^{2}+2\right)+\frac{1}{2 x^{2}+2}-\frac{26}{x^{2}+2}"," ",0,"5/2*x^2-7/2*ln(x^2+1)+1/2/(x^2+1)-26/(x^2+2)-10*ln(x^2+2)","A"
78,1,36,38,0.016000," ","int(x*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x)","4 \ln \left(x^{2}+1\right)-\frac{3 \ln \left(x^{2}+2\right)}{2}-\frac{1}{2 \left(x^{2}+1\right)}+\frac{13}{x^{2}+2}"," ",0,"4*ln(x^2+1)-1/2/(x^2+1)+13/(x^2+2)-3/2*ln(x^2+2)","A"
79,1,38,40,0.016000," ","int((5*x^6+3*x^4+x^2+4)/x/(x^4+3*x^2+2)^2,x)","\ln \left(x \right)-\frac{9 \ln \left(x^{2}+1\right)}{2}+4 \ln \left(x^{2}+2\right)+\frac{1}{2 x^{2}+2}-\frac{13}{2 \left(x^{2}+2\right)}"," ",0,"ln(x)-9/2*ln(x^2+1)+1/2/(x^2+1)-13/2/(x^2+2)+4*ln(x^2+2)","A"
80,1,45,47,0.017000," ","int((5*x^6+3*x^4+x^2+4)/x^3/(x^4+3*x^2+2)^2,x)","-\frac{11 \ln \left(x \right)}{4}+5 \ln \left(x^{2}+1\right)-\frac{29 \ln \left(x^{2}+2\right)}{8}-\frac{1}{2 x^{2}}-\frac{1}{2 \left(x^{2}+1\right)}+\frac{13}{4 \left(x^{2}+2\right)}"," ",0,"-1/2/x^2-11/4*ln(x)+5*ln(x^2+1)-1/2/(x^2+1)+13/4/(x^2+2)-29/8*ln(x^2+2)","A"
81,1,50,52,0.019000," ","int((5*x^6+3*x^4+x^2+4)/x^5/(x^4+3*x^2+2)^2,x)","\frac{23 \ln \left(x \right)}{4}-\frac{11 \ln \left(x^{2}+1\right)}{2}+\frac{21 \ln \left(x^{2}+2\right)}{8}+\frac{11}{8 x^{2}}-\frac{1}{4 x^{4}}+\frac{1}{2 x^{2}+2}-\frac{13}{8 \left(x^{2}+2\right)}"," ",0,"-1/4/x^4+11/8/x^2+23/4*ln(x)-11/2*ln(x^2+1)+1/2/(x^2+1)-13/8/(x^2+2)+21/8*ln(x^2+2)","A"
82,1,56,57,0.012000," ","int(x^8*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x)","\frac{5 x^{7}}{7}-\frac{27 x^{5}}{5}+\frac{98 x^{3}}{3}-293 x +\frac{x}{2 x^{2}+2}-\frac{104 x}{x^{2}+2}+\frac{9 \arctan \left(x \right)}{2}+340 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)"," ",0,"5/7*x^7-27/5*x^5+98/3*x^3-293*x+1/2*x/(x^2+1)+9/2*arctan(x)-104*x/(x^2+2)+340*arctan(1/2*2^(1/2)*x)*2^(1/2)","A"
83,1,49,50,0.012000," ","int(x^6*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x)","x^{5}-9 x^{3}+98 x -\frac{x}{2 \left(x^{2}+1\right)}+\frac{52 x}{x^{2}+2}-\frac{11 \arctan \left(x \right)}{2}-118 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)"," ",0,"x^5-9*x^3+98*x-1/2/(x^2+1)*x-11/2*arctan(x)+52/(x^2+2)*x-118*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
84,1,46,47,0.013000," ","int(x^4*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x)","\frac{5 x^{3}}{3}-27 x +\frac{x}{2 x^{2}+2}-\frac{26 x}{x^{2}+2}+\frac{13 \arctan \left(x \right)}{2}+33 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)"," ",0,"5/3*x^3-27*x+1/2/(x^2+1)*x+13/2*arctan(x)-26/(x^2+2)*x+33*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
85,1,41,42,0.011000," ","int(x^2*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x)","5 x -\frac{x}{2 \left(x^{2}+1\right)}+\frac{13 x}{x^{2}+2}-\frac{15 \arctan \left(x \right)}{2}-\frac{7 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{2}"," ",0,"5*x-1/2/(x^2+1)*x-15/2*arctan(x)+13/(x^2+2)*x-7/2*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
86,1,38,39,0.012000," ","int((5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^2,x)","\frac{x}{2 x^{2}+2}-\frac{13 x}{2 \left(x^{2}+2\right)}+\frac{17 \arctan \left(x \right)}{2}-\frac{19 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{4}"," ",0,"1/2/(x^2+1)*x+17/2*arctan(x)-13/2/(x^2+2)*x-19/4*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
87,1,43,44,0.013000," ","int((5*x^6+3*x^4+x^2+4)/x^2/(x^4+3*x^2+2)^2,x)","-\frac{x}{2 \left(x^{2}+1\right)}+\frac{13 x}{4 \left(x^{2}+2\right)}-\frac{19 \arctan \left(x \right)}{2}+\frac{45 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{8}-\frac{1}{x}"," ",0,"-1/x-1/2/(x^2+1)*x-19/2*arctan(x)+13/4/(x^2+2)*x+45/8*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
88,1,48,49,0.015000," ","int((5*x^6+3*x^4+x^2+4)/x^4/(x^4+3*x^2+2)^2,x)","\frac{x}{2 x^{2}+2}-\frac{13 x}{8 \left(x^{2}+2\right)}+\frac{21 \arctan \left(x \right)}{2}-\frac{71 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{16}+\frac{11}{4 x}-\frac{1}{3 x^{3}}"," ",0,"-1/3/x^3+11/4/x+1/2/(x^2+1)*x+21/2*arctan(x)-13/8/(x^2+2)*x-71/16*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
89,1,53,54,0.017000," ","int((5*x^6+3*x^4+x^2+4)/x^6/(x^4+3*x^2+2)^2,x)","-\frac{x}{2 \left(x^{2}+1\right)}+\frac{13 x}{16 \left(x^{2}+2\right)}-\frac{23 \arctan \left(x \right)}{2}+\frac{97 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{32}-\frac{23}{4 x}+\frac{11}{12 x^{3}}-\frac{1}{5 x^{5}}"," ",0,"-1/5/x^5+11/12/x^3-23/4/x-1/2/(x^2+1)*x-23/2*arctan(x)+13/16/(x^2+2)*x+97/32*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
90,1,58,59,0.016000," ","int((5*x^6+3*x^4+x^2+4)/x^8/(x^4+3*x^2+2)^2,x)","\frac{x}{2 x^{2}+2}-\frac{13 x}{32 \left(x^{2}+2\right)}+\frac{25 \arctan \left(x \right)}{2}-\frac{123 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{64}+\frac{137}{16 x}-\frac{23}{12 x^{3}}+\frac{11}{20 x^{5}}-\frac{1}{7 x^{7}}"," ",0,"-1/7/x^7+11/20/x^5-23/12/x^3+137/16/x+1/2/(x^2+1)*x+25/2*arctan(x)-13/32/(x^2+2)*x-123/64*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
91,1,64,72,0.013000," ","int(x^10*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x)","x^{5}-14 x^{3}+214 x +\frac{477 \arctan \left(x \right)}{8}-351 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)+\frac{-\frac{11}{8} x^{3}-\frac{13}{8} x}{\left(x^{2}+1\right)^{2}}-\frac{16 \left(-\frac{105}{8} x^{3}-\frac{79}{4} x \right)}{\left(x^{2}+2\right)^{2}}"," ",0,"x^5-14*x^3+214*x+(-11/8*x^3-13/8*x)/(x^2+1)^2+477/8*arctan(x)-16*(-105/8*x^3-79/4*x)/(x^2+2)^2-351*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
92,1,62,69,0.013000," ","int(x^8*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x)","\frac{5 x^{3}}{3}-42 x -\frac{449 \arctan \left(x \right)}{8}+\frac{219 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{2}-\frac{-\frac{15}{8} x^{3}-\frac{17}{8} x}{\left(x^{2}+1\right)^{2}}+\frac{-53 x^{3}-54 x}{\left(x^{2}+2\right)^{2}}"," ",0,"5/3*x^3-42*x-(-15/8*x^3-17/8*x)/(x^2+1)^2-449/8*arctan(x)+16*(-53/16*x^3-27/8*x)/(x^2+2)^2+219/2*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
93,1,56,64,0.013000," ","int(x^6*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x)","5 x +\frac{413 \arctan \left(x \right)}{8}-\frac{191 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{4}+\frac{-\frac{19}{8} x^{3}-\frac{21}{8} x}{\left(x^{2}+1\right)^{2}}-\frac{16 \left(-\frac{1}{32} x^{3}+\frac{25}{16} x \right)}{\left(x^{2}+2\right)^{2}}"," ",0,"5*x+(-19/8*x^3-21/8*x)/(x^2+1)^2+413/8*arctan(x)-16*(-1/32*x^3+25/16*x)/(x^2+2)^2-191/4*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
94,1,54,61,0.011000," ","int(x^4*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x)","-\frac{369 \arctan \left(x \right)}{8}+\frac{267 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{8}-\frac{-\frac{23}{8} x^{3}-\frac{25}{8} x}{\left(x^{2}+1\right)^{2}}+\frac{\frac{51}{4} x^{3}+\frac{77}{2} x}{\left(x^{2}+2\right)^{2}}"," ",0,"-(-23/8*x^3-25/8*x)/(x^2+1)^2-369/8*arctan(x)+2*(51/8*x^3+77/4*x)/(x^2+2)^2+267/8*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
95,1,53,61,0.013000," ","int(x^2*(5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x)","\frac{317 \arctan \left(x \right)}{8}-\frac{447 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{16}+\frac{-\frac{27}{8} x^{3}-\frac{29}{8} x}{\left(x^{2}+1\right)^{2}}-\frac{\frac{103}{8} x^{3}+\frac{129}{4} x}{\left(x^{2}+2\right)^{2}}"," ",0,"(-27/8*x^3-29/8*x)/(x^2+1)^2+317/8*arctan(x)-(103/8*x^3+129/4*x)/(x^2+2)^2-447/16*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
96,1,53,61,0.013000," ","int((5*x^6+3*x^4+x^2+4)/(x^4+3*x^2+2)^3,x)","-\frac{257 \arctan \left(x \right)}{8}+\frac{731 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{32}-\frac{-\frac{31}{8} x^{3}-\frac{33}{8} x}{\left(x^{2}+1\right)^{2}}+\frac{\frac{155}{16} x^{3}+\frac{181}{8} x}{\left(x^{2}+2\right)^{2}}"," ",0,"-(-31/8*x^3-33/8*x)/(x^2+1)^2-257/8*arctan(x)+(155/16*x^3+181/8*x)/(x^2+2)^2+731/32*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
97,1,58,66,0.014000," ","int((5*x^6+3*x^4+x^2+4)/x^2/(x^4+3*x^2+2)^3,x)","\frac{189 \arctan \left(x \right)}{8}-\frac{1119 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{64}-\frac{1}{2 x}+\frac{-\frac{35}{8} x^{3}-\frac{37}{8} x}{\left(x^{2}+1\right)^{2}}-\frac{\frac{207}{16} x^{3}+\frac{233}{8} x}{2 \left(x^{2}+2\right)^{2}}"," ",0,"-1/2/x+(-35/8*x^3-37/8*x)/(x^2+1)^2+189/8*arctan(x)-1/2*(207/16*x^3+233/8*x)/(x^2+2)^2-1119/64*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
98,1,64,71,0.016000," ","int((5*x^6+3*x^4+x^2+4)/x^4/(x^4+3*x^2+2)^3,x)","-\frac{113 \arctan \left(x \right)}{8}+\frac{1611 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{128}+\frac{17}{8 x}-\frac{1}{6 x^{3}}-\frac{-\frac{39}{8} x^{3}-\frac{41}{8} x}{\left(x^{2}+1\right)^{2}}+\frac{\frac{259}{8} x^{3}+\frac{285}{4} x}{8 \left(x^{2}+2\right)^{2}}"," ",0,"-1/6/x^3+17/8/x-(-39/8*x^3-41/8*x)/(x^2+1)^2-113/8*arctan(x)+1/8*(259/8*x^3+285/4*x)/(x^2+2)^2+1611/128*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
99,1,68,76,0.015000," ","int((5*x^6+3*x^4+x^2+4)/x^6/(x^4+3*x^2+2)^3,x)","\frac{29 \arctan \left(x \right)}{8}-\frac{2207 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{2}\right)}{256}-\frac{93}{16 x}+\frac{17}{24 x^{3}}-\frac{1}{10 x^{5}}+\frac{-\frac{43}{8} x^{3}-\frac{45}{8} x}{\left(x^{2}+1\right)^{2}}-\frac{\frac{311}{8} x^{3}+\frac{337}{4} x}{16 \left(x^{2}+2\right)^{2}}"," ",0,"-1/10/x^5+17/24/x^3-93/16/x+(-43/8*x^3-45/8*x)/(x^2+1)^2+29/8*arctan(x)-1/16*(311/8*x^3+337/4*x)/(x^2+2)^2-2207/256*2^(1/2)*arctan(1/2*2^(1/2)*x)","A"
100,1,74,71,0.010000," ","int(x^9*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x)","\frac{5 x^{8}}{8}-\frac{17 x^{6}}{6}+\frac{19 x^{4}}{4}+19 x^{2}+\frac{201 \sqrt{2}\, \arctan \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4}\right)}{16}-\frac{183 \ln \left(x^{4}+2 x^{2}+3\right)}{4}-\frac{\frac{175 x^{2}}{4}+\frac{375}{4}}{2 \left(x^{4}+2 x^{2}+3\right)}"," ",0,"5/8*x^8-17/6*x^6+19/4*x^4+19*x^2-1/2*(175/4*x^2+375/4)/(x^4+2*x^2+3)-183/4*ln(x^4+2*x^2+3)+201/16*2^(1/2)*arctan(1/4*(2*x^2+2)*2^(1/2))","A"
101,1,69,66,0.009000," ","int(x^7*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x)","\frac{5 x^{6}}{6}-\frac{17 x^{4}}{4}+\frac{19 x^{2}}{2}-\frac{455 \sqrt{2}\, \arctan \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4}\right)}{16}+\frac{19 \ln \left(x^{4}+2 x^{2}+3\right)}{2}+\frac{\frac{125 x^{2}}{4}+\frac{75}{4}}{2 x^{4}+4 x^{2}+6}"," ",0,"5/6*x^6-17/4*x^4+19/2*x^2+1/2*(125/4*x^2+75/4)/(x^4+2*x^2+3)+19/2*ln(x^4+2*x^2+3)-455/16*2^(1/2)*arctan(1/4*(2*x^2+2)*2^(1/2))","A"
102,1,64,61,0.009000," ","int(x^5*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x)","\frac{5 x^{4}}{4}-\frac{17 x^{2}}{2}+\frac{203 \sqrt{2}\, \arctan \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4}\right)}{16}+\frac{19 \ln \left(x^{4}+2 x^{2}+3\right)}{4}+\frac{-\frac{25 x^{2}}{4}+\frac{75}{4}}{2 x^{4}+4 x^{2}+6}"," ",0,"5/4*x^4-17/2*x^2+1/2*(-25/4*x^2+75/4)/(x^4+2*x^2+3)+19/4*ln(x^4+2*x^2+3)+203/16*2^(1/2)*arctan(1/4*(2*x^2+2)*2^(1/2))","A"
103,1,59,54,0.010000," ","int(x^3*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x)","\frac{5 x^{2}}{2}-\frac{17 \sqrt{2}\, \arctan \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4}\right)}{16}-\frac{17 \ln \left(x^{4}+2 x^{2}+3\right)}{4}-\frac{\frac{25 x^{2}}{4}+\frac{75}{4}}{2 \left(x^{4}+2 x^{2}+3\right)}"," ",0,"5/2*x^2-1/2*(25/4*x^2+75/4)/(x^4+2*x^2+3)-17/4*ln(x^4+2*x^2+3)-17/16*2^(1/2)*arctan(1/4*(2*x^2+2)*2^(1/2))","A"
104,1,54,49,0.010000," ","int(x*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x)","-\frac{23 \sqrt{2}\, \arctan \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4}\right)}{16}+\frac{5 \ln \left(x^{4}+2 x^{2}+3\right)}{4}+\frac{\frac{25 x^{2}}{4}+\frac{25}{4}}{2 x^{4}+4 x^{2}+6}"," ",0,"1/2*(25/4*x^2+25/4)/(x^4+2*x^2+3)+5/4*ln(x^4+2*x^2+3)-23/16*2^(1/2)*arctan(1/4*(2*x^2+2)*2^(1/2))","A"
105,1,58,55,0.012000," ","int((5*x^6+3*x^4+x^2+4)/x/(x^4+2*x^2+3)^2,x)","\frac{89 \sqrt{2}\, \arctan \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4}\right)}{144}+\frac{4 \ln \left(x \right)}{9}-\frac{\ln \left(x^{4}+2 x^{2}+3\right)}{9}-\frac{\frac{75 x^{2}}{4}-\frac{75}{4}}{18 \left(x^{4}+2 x^{2}+3\right)}"," ",0,"4/9*ln(x)-1/18*(75/4*x^2-75/4)/(x^4+2*x^2+3)-1/9*ln(x^4+2*x^2+3)+89/144*2^(1/2)*arctan(1/4*(2*x^2+2)*2^(1/2))","A"
106,1,63,58,0.013000," ","int((5*x^6+3*x^4+x^2+4)/x^3/(x^4+2*x^2+3)^2,x)","-\frac{71 \sqrt{2}\, \arctan \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4}\right)}{432}-\frac{13 \ln \left(x \right)}{27}+\frac{13 \ln \left(x^{4}+2 x^{2}+3\right)}{108}-\frac{2}{9 x^{2}}+\frac{-\frac{75 x^{2}}{4}-\frac{375}{4}}{54 x^{4}+108 x^{2}+162}"," ",0,"-2/9/x^2-13/27*ln(x)+1/54*(-75/4*x^2-375/4)/(x^4+2*x^2+3)+13/108*ln(x^4+2*x^2+3)-71/432*2^(1/2)*arctan(1/4*(2*x^2+2)*2^(1/2))","A"
107,1,68,65,0.014000," ","int((5*x^6+3*x^4+x^2+4)/x^5/(x^4+2*x^2+3)^2,x)","\frac{125 \sqrt{2}\, \arctan \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4}\right)}{432}+\frac{13 \ln \left(x \right)}{27}-\frac{13 \ln \left(x^{4}+2 x^{2}+3\right)}{108}+\frac{13}{54 x^{2}}-\frac{1}{9 x^{4}}-\frac{-\frac{125 x^{2}}{4}-\frac{175}{4}}{54 \left(x^{4}+2 x^{2}+3\right)}"," ",0,"-1/9/x^4+13/54/x^2+13/27*ln(x)-1/54*(-125/4*x^2-175/4)/(x^4+2*x^2+3)-13/108*ln(x^4+2*x^2+3)+125/432*2^(1/2)*arctan(1/4*(2*x^2+2)*2^(1/2))","A"
108,1,73,70,0.014000," ","int((5*x^6+3*x^4+x^2+4)/x^7/(x^4+2*x^2+3)^2,x)","-\frac{1237 \sqrt{2}\, \arctan \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4}\right)}{3888}+\frac{61 \ln \left(x \right)}{243}-\frac{61 \ln \left(x^{4}+2 x^{2}+3\right)}{972}-\frac{13}{54 x^{2}}+\frac{13}{108 x^{4}}-\frac{2}{27 x^{6}}-\frac{\frac{525 x^{2}}{4}-\frac{75}{4}}{486 \left(x^{4}+2 x^{2}+3\right)}"," ",0,"-2/27/x^6+13/108/x^4-13/54/x^2+61/243*ln(x)-1/486*(525/4*x^2-75/4)/(x^4+2*x^2+3)-61/972*ln(x^4+2*x^2+3)-1237/3888*2^(1/2)*arctan(1/4*(2*x^2+2)*2^(1/2))","A"
109,1,427,172,0.119000," ","int(x^8*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x)","\frac{5 x^{7}}{7}-\frac{17 x^{5}}{5}+\frac{19 x^{3}}{3}+38 x -\frac{505 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{32 \sqrt{2+2 \sqrt{3}}}-\frac{11 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{2 \sqrt{2+2 \sqrt{3}}}-\frac{329 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{8 \sqrt{2+2 \sqrt{3}}}-\frac{505 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{32 \sqrt{2+2 \sqrt{3}}}-\frac{11 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{2 \sqrt{2+2 \sqrt{3}}}-\frac{329 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{8 \sqrt{2+2 \sqrt{3}}}-\frac{505 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{64}-\frac{11 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{4}+\frac{505 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{64}+\frac{11 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{4}-\frac{-\frac{125}{8} x^{3}-\frac{75}{8} x}{x^{4}+2 x^{2}+3}"," ",0,"5/7*x^7-17/5*x^5+19/3*x^3+38*x-(-125/8*x^3-75/8*x)/(x^4+2*x^2+3)-505/64*ln(x^2+3^(1/2)-x*(-2+2*3^(1/2))^(1/2))*(-2+2*3^(1/2))^(1/2)*3^(1/2)-11/4*ln(x^2+3^(1/2)-x*(-2+2*3^(1/2))^(1/2))*(-2+2*3^(1/2))^(1/2)-505/32/(2+2*3^(1/2))^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))*(-2+2*3^(1/2))*3^(1/2)-11/2/(2+2*3^(1/2))^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))*(-2+2*3^(1/2))-329/8/(2+2*3^(1/2))^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))*3^(1/2)+505/64*ln(x^2+3^(1/2)+x*(-2+2*3^(1/2))^(1/2))*(-2+2*3^(1/2))^(1/2)*3^(1/2)+11/4*ln(x^2+3^(1/2)+x*(-2+2*3^(1/2))^(1/2))*(-2+2*3^(1/2))^(1/2)-505/32/(2+2*3^(1/2))^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))*(-2+2*3^(1/2))*3^(1/2)-11/2/(2+2*3^(1/2))^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))*(-2+2*3^(1/2))-329/8/(2+2*3^(1/2))^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))*3^(1/2)","B"
110,1,419,165,0.032000," ","int(x^6*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x)","x^{5}-\frac{17 x^{3}}{3}+19 x +\frac{57 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{8 \sqrt{2+2 \sqrt{3}}}+\frac{405 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{32 \sqrt{2+2 \sqrt{3}}}-\frac{177 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{8 \sqrt{2+2 \sqrt{3}}}+\frac{57 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{8 \sqrt{2+2 \sqrt{3}}}+\frac{405 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{32 \sqrt{2+2 \sqrt{3}}}-\frac{177 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{8 \sqrt{2+2 \sqrt{3}}}+\frac{57 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{16}+\frac{405 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{64}-\frac{57 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{16}-\frac{405 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{64}+\frac{-\frac{25}{8} x^{3}+\frac{75}{8} x}{x^{4}+2 x^{2}+3}"," ",0,"x^5-17/3*x^3+19*x+(-25/8*x^3+75/8*x)/(x^4+2*x^2+3)+57/16*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+405/64*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+57/8/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+405/32/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-177/8/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-57/16*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-405/64*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+57/8/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+405/32/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-177/8/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
111,1,416,160,0.030000," ","int(x^4*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x)","\frac{5 x^{3}}{3}-17 x -\frac{17 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{32 \sqrt{2+2 \sqrt{3}}}-\frac{89 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{16 \sqrt{2+2 \sqrt{3}}}+\frac{161 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{8 \sqrt{2+2 \sqrt{3}}}-\frac{17 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{32 \sqrt{2+2 \sqrt{3}}}-\frac{89 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{16 \sqrt{2+2 \sqrt{3}}}+\frac{161 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{8 \sqrt{2+2 \sqrt{3}}}-\frac{17 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{64}-\frac{89 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{32}+\frac{17 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{64}+\frac{89 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{32}+\frac{-\frac{25}{8} x^{3}-\frac{75}{8} x}{x^{4}+2 x^{2}+3}"," ",0,"5/3*x^3-17*x+(-25/8*x^3-75/8*x)/(x^4+2*x^2+3)-17/64*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-89/32*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-17/32/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-89/16/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+161/8/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+17/64*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+89/32*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-17/32/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-89/16/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+161/8/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
112,1,412,155,0.034000," ","int(x^2*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x)","5 x -\frac{47 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{48 \sqrt{2+2 \sqrt{3}}}+\frac{17 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{32 \sqrt{2+2 \sqrt{3}}}-\frac{145 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{24 \sqrt{2+2 \sqrt{3}}}-\frac{47 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{48 \sqrt{2+2 \sqrt{3}}}+\frac{17 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{32 \sqrt{2+2 \sqrt{3}}}-\frac{145 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{24 \sqrt{2+2 \sqrt{3}}}-\frac{47 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{96}+\frac{17 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{64}+\frac{47 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{96}-\frac{17 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{64}-\frac{-\frac{25}{8} x^{3}-\frac{25}{8} x}{x^{4}+2 x^{2}+3}"," ",0,"5*x-(-25/8*x^3-25/8*x)/(x^4+2*x^2+3)-47/96*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+17/64*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-47/48/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+17/32/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-145/24/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+47/96*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-17/64*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-47/48/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+17/32/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-145/24/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
113,1,408,154,0.029000," ","int((5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^2,x)","\frac{139 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{288 \sqrt{2+2 \sqrt{3}}}+\frac{11 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{24 \sqrt{2+2 \sqrt{3}}}+\frac{7 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{72 \sqrt{2+2 \sqrt{3}}}+\frac{139 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{288 \sqrt{2+2 \sqrt{3}}}+\frac{11 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{24 \sqrt{2+2 \sqrt{3}}}+\frac{7 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{72 \sqrt{2+2 \sqrt{3}}}+\frac{139 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{576}+\frac{11 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{48}-\frac{139 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{576}-\frac{11 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{48}+\frac{-\frac{25}{24} x^{3}+\frac{25}{24} x}{x^{4}+2 x^{2}+3}"," ",0,"(-25/24*x^3+25/24*x)/(x^4+2*x^2+3)+139/576*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+11/48*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+139/288/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+11/24/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+7/72/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-139/576*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-11/48*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+139/288/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+11/24/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+7/72/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
114,1,414,157,0.033000," ","int((5*x^6+3*x^4+x^2+4)/x^2/(x^4+2*x^2+3)^2,x)","-\frac{\left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{9 \sqrt{2+2 \sqrt{3}}}-\frac{13 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{96 \sqrt{2+2 \sqrt{3}}}+\frac{7 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{72 \sqrt{2+2 \sqrt{3}}}-\frac{\left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{9 \sqrt{2+2 \sqrt{3}}}-\frac{13 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{96 \sqrt{2+2 \sqrt{3}}}+\frac{7 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{72 \sqrt{2+2 \sqrt{3}}}-\frac{\sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{18}-\frac{13 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{192}+\frac{\sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{18}+\frac{13 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{192}-\frac{4}{9 x}-\frac{\frac{25}{8} x^{3}+\frac{125}{8} x}{9 \left(x^{4}+2 x^{2}+3\right)}"," ",0,"-4/9/x-1/9*(25/8*x^3+125/8*x)/(x^4+2*x^2+3)-1/18*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-13/192*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-1/9/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-13/96/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+7/72/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+1/18*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+13/192*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-1/9/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-13/96/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+7/72/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
115,1,419,164,0.035000," ","int((5*x^6+3*x^4+x^2+4)/x^4/(x^4+2*x^2+3)^2,x)","\frac{275 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{2592 \sqrt{2+2 \sqrt{3}}}+\frac{23 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{432 \sqrt{2+2 \sqrt{3}}}+\frac{137 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{648 \sqrt{2+2 \sqrt{3}}}+\frac{275 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{2592 \sqrt{2+2 \sqrt{3}}}+\frac{23 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{432 \sqrt{2+2 \sqrt{3}}}+\frac{137 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{648 \sqrt{2+2 \sqrt{3}}}+\frac{275 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{5184}+\frac{23 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{864}-\frac{275 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{5184}-\frac{23 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{864}+\frac{13}{27 x}-\frac{4}{27 x^{3}}+\frac{\frac{125}{8} x^{3}+\frac{175}{8} x}{27 x^{4}+54 x^{2}+81}"," ",0,"-4/27/x^3+13/27/x+1/27*(125/8*x^3+175/8*x)/(x^4+2*x^2+3)+275/5184*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+23/864*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+275/2592/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+23/432/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+137/648/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-275/5184*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-23/864*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+275/2592/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+23/432/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+137/648/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
116,1,424,169,0.034000," ","int((5*x^6+3*x^4+x^2+4)/x^6/(x^4+2*x^2+3)^2,x)","-\frac{481 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{3888 \sqrt{2+2 \sqrt{3}}}-\frac{475 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{2592 \sqrt{2+2 \sqrt{3}}}+\frac{463 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{1944 \sqrt{2+2 \sqrt{3}}}-\frac{481 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{3888 \sqrt{2+2 \sqrt{3}}}-\frac{475 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{2592 \sqrt{2+2 \sqrt{3}}}+\frac{463 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{1944 \sqrt{2+2 \sqrt{3}}}-\frac{481 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{7776}-\frac{475 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{5184}+\frac{481 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{7776}+\frac{475 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{5184}-\frac{13}{27 x}+\frac{13}{81 x^{3}}-\frac{4}{45 x^{5}}-\frac{\frac{175}{24} x^{3}-\frac{25}{24} x}{27 \left(x^{4}+2 x^{2}+3\right)}"," ",0,"-4/45/x^5+13/81/x^3-13/27/x-1/27*(175/24*x^3-25/24*x)/(x^4+2*x^2+3)-481/7776*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-475/5184*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-481/3888/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-475/2592/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+463/1944/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+481/7776*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+475/5184*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-481/3888/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-475/2592/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+463/1944/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
117,1,429,187,0.035000," ","int(x^10*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x)","x^{5}-9 x^{3}+58 x +\frac{5091 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}+\frac{14385 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}-\frac{4647 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{64 \sqrt{2+2 \sqrt{3}}}+\frac{5091 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}+\frac{14385 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}-\frac{4647 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{64 \sqrt{2+2 \sqrt{3}}}+\frac{5091 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}+\frac{14385 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}-\frac{5091 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}-\frac{14385 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}+\frac{\frac{63}{16} x^{7}+\frac{3809}{64} x^{5}+\frac{3333}{32} x^{3}+\frac{8415}{64} x}{\left(x^{4}+2 x^{2}+3\right)^{2}}"," ",0,"x^5-9*x^3+58*x+(63/16*x^7+3809/64*x^5+3333/32*x^3+8415/64*x)/(x^4+2*x^2+3)^2+5091/1024*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+14385/1024*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+5091/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+14385/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-4647/64/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-5091/1024*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-14385/1024*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+5091/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+14385/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-4647/64/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
118,1,426,184,0.033000," ","int(x^8*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x)","\frac{5 x^{3}}{3}-27 x +\frac{693 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}-\frac{3675 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}+\frac{273 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{8 \sqrt{2+2 \sqrt{3}}}+\frac{693 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}-\frac{3675 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}+\frac{273 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{8 \sqrt{2+2 \sqrt{3}}}+\frac{693 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}-\frac{3675 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}-\frac{693 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}+\frac{3675 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}+\frac{-\frac{835}{64} x^{7}-\frac{1569}{32} x^{5}-\frac{4941}{64} x^{3}-\frac{513}{8} x}{\left(x^{4}+2 x^{2}+3\right)^{2}}"," ",0,"5/3*x^3-27*x+(-835/64*x^7-1569/32*x^5-4941/64*x^3-513/8*x)/(x^4+2*x^2+3)^2+693/1024*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-3675/1024*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+693/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-3675/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+273/8/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-693/1024*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+3675/1024*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+693/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-3675/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+273/8/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
119,1,422,179,0.035000," ","int(x^6*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x)","5 x -\frac{943 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}-\frac{185 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}-\frac{379 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{64 \sqrt{2+2 \sqrt{3}}}-\frac{943 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}-\frac{185 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}-\frac{379 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{64 \sqrt{2+2 \sqrt{3}}}-\frac{943 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}-\frac{185 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}+\frac{943 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}+\frac{185 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}-\frac{-\frac{203}{32} x^{7}-\frac{889}{64} x^{5}-\frac{159}{8} x^{3}-\frac{531}{64} x}{\left(x^{4}+2 x^{2}+3\right)^{2}}"," ",0,"5*x-(-203/32*x^7-889/64*x^5-159/8*x^3-531/64*x)/(x^4+2*x^2+3)^2-943/1024*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-185/1024*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-943/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-185/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-379/64/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+943/1024*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+185/1024*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-943/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-185/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-379/64/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
120,1,418,174,0.032000," ","int(x^4*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x)","\frac{307 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}+\frac{399 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}-\frac{23 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{32 \sqrt{2+2 \sqrt{3}}}+\frac{307 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}+\frac{399 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}-\frac{23 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{32 \sqrt{2+2 \sqrt{3}}}+\frac{307 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}+\frac{399 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}-\frac{307 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}-\frac{399 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}+\frac{-\frac{59}{64} x^{7}+\frac{15}{8} x^{5}+\frac{199}{64} x^{3}+\frac{207}{32} x}{\left(x^{4}+2 x^{2}+3\right)^{2}}"," ",0,"(-59/64*x^7+15/8*x^5+199/64*x^3+207/32*x)/(x^4+2*x^2+3)^2+307/1024*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+399/1024*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+307/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+399/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-23/32/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-307/1024*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-399/1024*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+307/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+399/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-23/32/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
121,1,418,174,0.032000," ","int(x^2*(5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x)","-\frac{517 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{4608 \sqrt{2+2 \sqrt{3}}}-\frac{341 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{1536 \sqrt{2+2 \sqrt{3}}}+\frac{253 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{576 \sqrt{2+2 \sqrt{3}}}-\frac{517 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{4608 \sqrt{2+2 \sqrt{3}}}-\frac{341 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{1536 \sqrt{2+2 \sqrt{3}}}+\frac{253 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{576 \sqrt{2+2 \sqrt{3}}}-\frac{517 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{9216}-\frac{341 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{3072}+\frac{517 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{9216}+\frac{341 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{3072}+\frac{-\frac{11}{24} x^{7}-\frac{529}{192} x^{5}-\frac{335}{96} x^{3}-\frac{253}{64} x}{\left(x^{4}+2 x^{2}+3\right)^{2}}"," ",0,"(-11/24*x^7-529/192*x^5-335/96*x^3-253/64*x)/(x^4+2*x^2+3)^2-517/9216*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-341/3072*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-517/4608/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-341/1536/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+253/576/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+517/9216*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+341/3072*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-517/4608/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-341/1536/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+253/576/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
122,1,418,176,0.032000," ","int((5*x^6+3*x^4+x^2+4)/(x^4+2*x^2+3)^3,x)","\frac{55 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{1536 \sqrt{2+2 \sqrt{3}}}+\frac{21 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}-\frac{\sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{48 \sqrt{2+2 \sqrt{3}}}+\frac{55 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{1536 \sqrt{2+2 \sqrt{3}}}+\frac{21 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{512 \sqrt{2+2 \sqrt{3}}}-\frac{\sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{48 \sqrt{2+2 \sqrt{3}}}+\frac{55 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{3072}+\frac{21 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}-\frac{55 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{3072}-\frac{21 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{1024}+\frac{\frac{17}{64} x^{7}+\frac{83}{96} x^{5}+\frac{181}{192} x^{3}+\frac{73}{48} x}{\left(x^{4}+2 x^{2}+3\right)^{2}}"," ",0,"(17/64*x^7+83/96*x^5+181/192*x^3+73/48*x)/(x^4+2*x^2+3)^2+55/3072*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+21/1024*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+55/1536/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+21/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-1/48/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-55/3072*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-21/1024*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+55/1536/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+21/512/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-1/48/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
123,1,424,179,0.034000," ","int((5*x^6+3*x^4+x^2+4)/x^2/(x^4+2*x^2+3)^3,x)","-\frac{325 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{13824 \sqrt{2+2 \sqrt{3}}}+\frac{7 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{4608 \sqrt{2+2 \sqrt{3}}}-\frac{173 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{1728 \sqrt{2+2 \sqrt{3}}}-\frac{325 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{13824 \sqrt{2+2 \sqrt{3}}}+\frac{7 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{4608 \sqrt{2+2 \sqrt{3}}}-\frac{173 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{1728 \sqrt{2+2 \sqrt{3}}}-\frac{325 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{27648}+\frac{7 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{9216}+\frac{325 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{27648}-\frac{7 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{9216}-\frac{4}{27 x}-\frac{\frac{121}{32} x^{7}+\frac{809}{64} x^{5}+\frac{419}{16} x^{3}+\frac{2475}{64} x}{27 \left(x^{4}+2 x^{2}+3\right)^{2}}"," ",0,"-4/27/x-1/27*(121/32*x^7+809/64*x^5+419/16*x^3+2475/64*x)/(x^4+2*x^2+3)^2-325/27648*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+7/9216*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-325/13824/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+7/4608/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-173/1728/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+325/27648*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-7/9216*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-325/13824/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+7/4608/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-173/1728/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
124,1,429,186,0.036000," ","int((5*x^6+3*x^4+x^2+4)/x^4/(x^4+2*x^2+3)^3,x)","\frac{4865 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{124416 \sqrt{2+2 \sqrt{3}}}+\frac{127 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{41472 \sqrt{2+2 \sqrt{3}}}+\frac{1121 \sqrt{3}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{7776 \sqrt{2+2 \sqrt{3}}}+\frac{4865 \left(-2+2 \sqrt{3}\right) \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{124416 \sqrt{2+2 \sqrt{3}}}+\frac{127 \left(-2+2 \sqrt{3}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{41472 \sqrt{2+2 \sqrt{3}}}+\frac{1121 \sqrt{3}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{3}}}{\sqrt{2+2 \sqrt{3}}}\right)}{7776 \sqrt{2+2 \sqrt{3}}}+\frac{4865 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{248832}+\frac{127 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{82944}-\frac{4865 \sqrt{-2+2 \sqrt{3}}\, \sqrt{3}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{248832}-\frac{127 \sqrt{-2+2 \sqrt{3}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{3}}\, x +\sqrt{3}\right)}{82944}+\frac{7}{27 x}-\frac{4}{81 x^{3}}+\frac{\frac{1025}{192} x^{7}+\frac{881}{48} x^{5}+\frac{7523}{192} x^{3}+\frac{1087}{32} x}{27 \left(x^{4}+2 x^{2}+3\right)^{2}}"," ",0,"-4/81/x^3+7/27/x+1/27*(1025/192*x^7+881/48*x^5+7523/192*x^3+1087/32*x)/(x^4+2*x^2+3)^2+4865/248832*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+127/82944*(-2+2*3^(1/2))^(1/2)*ln(x^2-(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+4865/124416/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+127/41472/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+1121/7776/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x-(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))-4865/248832*(-2+2*3^(1/2))^(1/2)*3^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))-127/82944*(-2+2*3^(1/2))^(1/2)*ln(x^2+(-2+2*3^(1/2))^(1/2)*x+3^(1/2))+4865/124416/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+127/41472/(2+2*3^(1/2))^(1/2)*(-2+2*3^(1/2))*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))+1121/7776/(2+2*3^(1/2))^(1/2)*3^(1/2)*arctan((2*x+(-2+2*3^(1/2))^(1/2))/(2+2*3^(1/2))^(1/2))","B"
125,1,357,137,0.006000," ","int(x*(g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{g \,x^{4}}{4 c}+\frac{3 a b g \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{a f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}-\frac{b^{3} g \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{3}}+\frac{b^{2} f \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{b e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c}-\frac{b g \,x^{2}}{2 c^{2}}+\frac{f \,x^{2}}{2 c}+\frac{d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{a g \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}+\frac{b^{2} g \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{3}}-\frac{b f \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}+\frac{e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c}"," ",0,"1/4*g*x^4/c-1/2/c^2*x^2*b*g+1/2/c*f*x^2-1/4/c^2*ln(c*x^4+b*x^2+a)*a*g+1/4/c^3*ln(c*x^4+b*x^2+a)*b^2*g-1/4*b/c^2*f*ln(c*x^4+b*x^2+a)+1/4/c*e*ln(c*x^4+b*x^2+a)+3/2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b*g-1/(4*a*c-b^2)^(1/2)*a/c*f*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))+1/(4*a*c-b^2)^(1/2)*d*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))-1/2/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*g+1/2/(4*a*c-b^2)^(1/2)*b^2/c^2*f*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))-1/2/(4*a*c-b^2)^(1/2)*b/c*e*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","B"
126,1,3028,547,0.060000," ","int(x^4*(g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","\text{output too large to display}"," ",0,"-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b^3/c*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+13/4/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*f-13/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a*b/c*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/3*g*x^3/c^2-5/4/c^3/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^5*g+6/c^2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*g-5/4/c^3/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^5*g-6/c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*g-2/c^3*x*b*g+1/c^2*f*x-2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a*b^2*g-13/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*b*g+17/2/c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^3*g-13/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*b*g+17/2/c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^3*g+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a*b/c*e*x+3/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a*b/c*f*x^3-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a*b^2/c^2*f*x-3/4/c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*f+1/4/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+3/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b^3/c^2*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b^2/c*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b^2*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+5/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*f+3/4/c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*f-1/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e+2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a*b*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a*d*x-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a*e*x^3-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b*d*x^3-3/2/c^2/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*x*b*g+1/2/c^3/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*b^3*g-5/4/c^3/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*g+7/2/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*g+5/4/c^3/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*g-7/2/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*g-1/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+3/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b^4/c^2*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*e-c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d-19/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*f-19/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a*b^2/c*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^3/c^2*f*x^3+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^2/c*e*x^3+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a^2/c*f*x-3/2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e+1/4/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+3/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+5/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a^2*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a^2*g+1/2/c^3/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b^4*g","B"
127,1,2300,430,0.047000," ","int(x^2*(g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","\frac{3 a b g \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{a f \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{b^{3} g \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{b^{2} f \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{b e \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{c d \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{5 \sqrt{2}\, a^{2} g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{5 \sqrt{2}\, a^{2} g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{19 \sqrt{2}\, a \,b^{2} g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{19 \sqrt{2}\, a \,b^{2} g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{2 \sqrt{2}\, a b f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, a b f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, b^{4} g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b^{4} g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, b^{3} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{3} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{a^{2} g x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{a \,b^{2} g x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{a b f x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}+\frac{13 \sqrt{2}\, a b g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{13 \sqrt{2}\, a b g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{a e x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{3 \sqrt{2}\, a f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, a f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, b^{3} g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b^{3} g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{b d x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{\sqrt{2}\, b e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{g x}{c^{2}}"," ",0,"-19/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*g-19/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2*g+g*x/c^2+3/4/c^2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*g+5/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*g-3/4/c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*g+5/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*g+1/4/(4*a*c-b^2)/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b^2/c*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b^2*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b*e-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*a*e+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b*d+1/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+13/4/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*g+3/4/c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*g+3/4/c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*g-13/4/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*g-1/2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*a*b^2*g+2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*f-1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e-1/4/(4*a*c-b^2)/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*f+1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a*b*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a*c*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b^3*g+1/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b^2*f+1/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*a^2*g+3/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a*b*g+1/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*a*b*f-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b^3/c*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*d-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a*f-3/2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*f+1/4/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-1/2/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+3/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)","B"
128,1,1760,406,0.053000," ","int((g*x^6+f*x^4+e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","\frac{2 \sqrt{2}\, a b g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, a b g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a c f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a c f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b^{2} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b^{3} g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{3} g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, a g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, a g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{-\frac{\left(2 a^{2} c g -a \,b^{2} g +a b c f -2 a \,c^{2} e +b \,c^{2} d \right) x^{3}}{2 \left(4 a c -b^{2}\right) a c}+\frac{\left(a^{2} b g -2 a^{2} c f +a b c e +2 a \,c^{2} d -b^{2} c d \right) x}{2 \left(4 a c -b^{2}\right) a c}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"-3/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c^2*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+(-1/2/a*(2*a^2*c*g-a*b^2*g+a*b*c*f-2*a*c^2*e+b*c^2*d)/(4*a*c-b^2)/c*x^3+1/2*(a^2*b*g-2*a^2*c*f+a*b*c*e+2*a*c^2*d-b^2*c*d)/a/c/(4*a*c-b^2)*x)/(c*x^4+b*x^2+a)+1/4/a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*b^2*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/4/(4*a*c-b^2)/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*g+2*a/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*g-1/4/(4*a*c-b^2)/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*g+1/4/(4*a*c-b^2)/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*g-1/4/(4*a*c-b^2)/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*g-3/2*a/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*g+3/2*a/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*g-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f-3/(4*a*c-b^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b^2*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+2*a/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*g-1/2/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/a/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-a/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f+1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*b*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*a*c*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b*c*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f+1/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)","B"
129,1,2045,416,0.055000," ","int((g*x^6+f*x^4+e*x^2+d)/x^2/(c*x^4+b*x^2+a)^2,x)","-\frac{b c e \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{c^{2} d \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{2} c d \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{b g \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{c f \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{\sqrt{2}\, a c g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a c g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b^{2} c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, b \,c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \sqrt{2}\, b^{3} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, b^{3} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, b^{2} g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{a g x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{b^{2} e x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{3 b c d x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{\sqrt{2}\, b c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{5 \sqrt{2}\, c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{5 \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{b^{3} d x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{3 \sqrt{2}\, b^{2} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{3 \sqrt{2}\, b^{2} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{b f x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{\sqrt{2}\, b g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{c e x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{\sqrt{2}\, c f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{d}{a^{2} x}"," ",0,"4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*b*c^2*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+4/a*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-3/4/a^2*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d-3/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a^2*b^3*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4/a*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*b^2*c*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/a^2*d/x-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*g+1/4/a*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-a*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*g-a*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*g-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a*c^2*d*x^3-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a*b^2*e*x+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a^2*b^3*d*x-1/2*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f+1/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*b*c*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f+1/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*b*c*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-3/4/a^2*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+3/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a^2*b^2*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*g+1/4/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*g+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*c*e*x+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b*f*x-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b*g-a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*g+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*c*f*x^3-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*g+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a^2*b^2*c*d*x^3+5/2/a*c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d-5/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*c^2*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-3/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c^2*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-3*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a*b*c*e*x^3-3/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a*b*c*d*x","B"
130,1,2503,496,0.067000," ","int((g*x^6+f*x^4+e*x^2+d)/x^4/(c*x^4+b*x^2+a)^2,x)","-\frac{b c f \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{c^{2} e \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{2} c e \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{3 b \,c^{2} d \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{b^{3} c d \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{3}}+\frac{c g \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{\sqrt{2}\, b^{2} c f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} c f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, b \,c^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, b \,c^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{7 \sqrt{2}\, c^{3} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{7 \sqrt{2}\, c^{3} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \sqrt{2}\, b^{3} c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, b^{3} c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{29 \sqrt{2}\, b^{2} c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{29 \sqrt{2}\, b^{2} c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{5 \sqrt{2}\, b^{4} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}+\frac{5 \sqrt{2}\, b^{4} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}+\frac{\sqrt{2}\, b c g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{b^{2} f x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{3 b c e x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{\sqrt{2}\, b c f \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c f \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{c^{2} d x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{5 \sqrt{2}\, c^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{5 \sqrt{2}\, c^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{b^{3} e x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{2 b^{2} c d x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{3 \sqrt{2}\, b^{2} c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{3 \sqrt{2}\, b^{2} c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{19 \sqrt{2}\, b \,c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{19 \sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{b^{4} d x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{3}}+\frac{5 \sqrt{2}\, b^{3} c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}-\frac{5 \sqrt{2}\, b^{3} c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}+\frac{b g x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{c f x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{\sqrt{2}\, c g \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c g \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{e}{a^{2} x}+\frac{2 b d}{a^{3} x}-\frac{d}{3 a^{2} x^{3}}"," ",0,"-1/3/a^2*d/x^3+c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*g+c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*g+2/a^3*b*d/x-1/2*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*g+1/2*c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*g-5/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a^3*b^3*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+7/a*c^3/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+1/4/a*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*f-3/4/a^2*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*b*c*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+3/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a^2*b^2*c*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+19/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a^2*b*c^2*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+7/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*c^3*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-19/4/a^2*c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+5/4/a^3*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*d+1/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*g+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b*g-29/4/a^2*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*b^2*c*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*b*c^2*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-3/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a^2*b^3*c*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+4/a*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-3/4/a^2*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e+1/4/a*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*f+5/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a^3*b^4*c*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+5/4/a^3*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4*d-29/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a^2*b^2*c^2*d*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a*b*c*f*x^3+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a^2*b^2*c*e*x^3+3/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a^2*b*c^2*d*x^3-3/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a*b*c*e*x+2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a^2*b^2*c*d*x-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a^3*b^3*c*d*x^3+5/2/a*c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e-5/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)/a*c^2*e*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-3/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c^2*f*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-3*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*f+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*c*f*x-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a*c^2*e*x^3-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a^3*b^4*d*x-1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a*b^2*f*x-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a*c^2*d*x+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)/a^2*b^3*e*x-1/a^2*e/x","B"
131,1,21,20,0.010000," ","int(x^2*(c*x^4+b*x^2+a)^p*(3*a+b*(5+2*p)*x^2+c*(7+4*p)*x^4),x)","x^{3} \left(c \,x^{4}+b \,x^{2}+a \right)^{p +1}"," ",0,"x^3*(c*x^4+b*x^2+a)^(p+1)","A"
132,1,145,182,0.009000," ","int(x^5*(c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{e x +d}\, \sqrt{-e x +d}\, \left(35 c \,x^{8} e^{8}+45 b \,e^{8} x^{6}+40 c \,d^{2} e^{6} x^{6}+63 a \,e^{8} x^{4}+54 b \,d^{2} e^{6} x^{4}+48 c \,d^{4} e^{4} x^{4}+84 a \,d^{2} e^{6} x^{2}+72 b \,d^{4} e^{4} x^{2}+64 c \,d^{6} e^{2} x^{2}+168 a \,d^{4} e^{4}+144 b \,d^{6} e^{2}+128 c \,d^{8}\right)}{315 e^{10}}"," ",0,"-1/315*(e*x+d)^(1/2)*(-e*x+d)^(1/2)*(35*c*e^8*x^8+45*b*e^8*x^6+40*c*d^2*e^6*x^6+63*a*e^8*x^4+54*b*d^2*e^6*x^4+48*c*d^4*e^4*x^4+84*a*d^2*e^6*x^2+72*b*d^4*e^4*x^2+64*c*d^6*e^2*x^2+168*a*d^4*e^4+144*b*d^6*e^2+128*c*d^8)/e^10","A"
133,1,109,137,0.007000," ","int(x^3*(c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{e x +d}\, \sqrt{-e x +d}\, \left(15 c \,x^{6} e^{6}+21 b \,e^{6} x^{4}+18 c \,d^{2} e^{4} x^{4}+35 a \,e^{6} x^{2}+28 b \,d^{2} e^{4} x^{2}+24 c \,d^{4} e^{2} x^{2}+70 a \,d^{2} e^{4}+56 b \,d^{4} e^{2}+48 c \,d^{6}\right)}{105 e^{8}}"," ",0,"-1/105*(e*x+d)^(1/2)*(-e*x+d)^(1/2)*(15*c*e^6*x^6+21*b*e^6*x^4+18*c*d^2*e^4*x^4+35*a*e^6*x^2+28*b*d^2*e^4*x^2+24*c*d^4*e^2*x^2+70*a*d^2*e^4+56*b*d^4*e^2+48*c*d^6)/e^8","A"
134,1,73,93,0.006000," ","int(x*(c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{e x +d}\, \sqrt{-e x +d}\, \left(3 c \,x^{4} e^{4}+5 b \,e^{4} x^{2}+4 c \,d^{2} e^{2} x^{2}+15 a \,e^{4}+10 b \,d^{2} e^{2}+8 c \,d^{4}\right)}{15 e^{6}}"," ",0,"-1/15*(e*x+d)^(1/2)*(-e*x+d)^(1/2)*(3*c*e^4*x^4+5*b*e^4*x^2+4*c*d^2*e^2*x^2+15*a*e^4+10*b*d^2*e^2+8*c*d^4)/e^6","A"
135,1,143,79,0.042000," ","int((c*x^4+b*x^2+a)/x/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{-e x +d}\, \sqrt{e x +d}\, \left(\sqrt{-e^{2} x^{2}+d^{2}}\, c d \,e^{2} x^{2} \mathrm{csgn}\left(d \right)+3 a \,e^{4} \ln \left(\frac{2 \left(d +\sqrt{-e^{2} x^{2}+d^{2}}\, \mathrm{csgn}\left(d \right)\right) d}{x}\right)+3 \sqrt{-e^{2} x^{2}+d^{2}}\, b d \,e^{2} \mathrm{csgn}\left(d \right)+2 \sqrt{-e^{2} x^{2}+d^{2}}\, c \,d^{3} \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d \,e^{4}}"," ",0,"-1/3*(-e*x+d)^(1/2)*(e*x+d)^(1/2)/d*(csgn(d)*x^2*c*d*e^2*(-e^2*x^2+d^2)^(1/2)+3*csgn(d)*(-e^2*x^2+d^2)^(1/2)*b*d*e^2+2*csgn(d)*(-e^2*x^2+d^2)^(1/2)*c*d^3+3*ln(2*d*((-e^2*x^2+d^2)^(1/2)*csgn(d)+d)/x)*a*e^4)*csgn(d)/(-e^2*x^2+d^2)^(1/2)/e^4","C"
136,1,163,83,0.024000," ","int((c*x^4+b*x^2+a)/x^3/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{-e x +d}\, \sqrt{e x +d}\, \left(a \,e^{4} x^{2} \ln \left(\frac{2 \left(d +\sqrt{-e^{2} x^{2}+d^{2}}\, \mathrm{csgn}\left(d \right)\right) d}{x}\right)+2 b \,d^{2} e^{2} x^{2} \ln \left(\frac{2 \left(d +\sqrt{-e^{2} x^{2}+d^{2}}\, \mathrm{csgn}\left(d \right)\right) d}{x}\right)+2 \sqrt{-e^{2} x^{2}+d^{2}}\, c \,d^{3} x^{2} \mathrm{csgn}\left(d \right)+\sqrt{-e^{2} x^{2}+d^{2}}\, a d \,e^{2} \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3} e^{2} x^{2}}"," ",0,"-1/2*(-e*x+d)^(1/2)*(e*x+d)^(1/2)/d^3*(2*csgn(d)*x^2*c*d^3*(-e^2*x^2+d^2)^(1/2)+ln(2*(d+(-e^2*x^2+d^2)^(1/2)*csgn(d))*d/x)*x^2*a*e^4+2*ln(2*(d+(-e^2*x^2+d^2)^(1/2)*csgn(d))*d/x)*x^2*b*d^2*e^2+csgn(d)*a*d*e^2*(-e^2*x^2+d^2)^(1/2))*csgn(d)/(-e^2*x^2+d^2)^(1/2)/e^2/x^2","C"
137,1,222,108,0.030000," ","int((c*x^4+b*x^2+a)/x^5/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{-e x +d}\, \sqrt{e x +d}\, \left(3 a \,e^{4} x^{4} \ln \left(\frac{2 \left(d +\sqrt{-e^{2} x^{2}+d^{2}}\, \mathrm{csgn}\left(d \right)\right) d}{x}\right)+4 b \,d^{2} e^{2} x^{4} \ln \left(\frac{2 \left(d +\sqrt{-e^{2} x^{2}+d^{2}}\, \mathrm{csgn}\left(d \right)\right) d}{x}\right)+8 c \,d^{4} x^{4} \ln \left(\frac{2 \left(d +\sqrt{-e^{2} x^{2}+d^{2}}\, \mathrm{csgn}\left(d \right)\right) d}{x}\right)+3 \sqrt{-e^{2} x^{2}+d^{2}}\, a d \,e^{2} x^{2} \mathrm{csgn}\left(d \right)+4 \sqrt{-e^{2} x^{2}+d^{2}}\, b \,d^{3} x^{2} \mathrm{csgn}\left(d \right)+2 \sqrt{-e^{2} x^{2}+d^{2}}\, a \,d^{3} \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{8 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{5} x^{4}}"," ",0,"-1/8*(-e*x+d)^(1/2)*(e*x+d)^(1/2)/d^5*(3*ln(2*(d+(-e^2*x^2+d^2)^(1/2)*csgn(d))*d/x)*x^4*a*e^4+4*ln(2*(d+(-e^2*x^2+d^2)^(1/2)*csgn(d))*d/x)*x^4*b*d^2*e^2+8*ln(2*(d+(-e^2*x^2+d^2)^(1/2)*csgn(d))*d/x)*x^4*c*d^4+3*csgn(d)*x^2*a*d*e^2*(-e^2*x^2+d^2)^(1/2)+4*csgn(d)*x^2*b*d^3*(-e^2*x^2+d^2)^(1/2)+2*csgn(d)*a*d^3*(-e^2*x^2+d^2)^(1/2))*csgn(d)/(-e^2*x^2+d^2)^(1/2)/x^4","C"
138,1,306,184,0.036000," ","int((c*x^4+b*x^2+a)/x^7/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{-e x +d}\, \sqrt{e x +d}\, \left(15 a \,e^{6} x^{6} \ln \left(\frac{2 \left(d +\sqrt{-e^{2} x^{2}+d^{2}}\, \mathrm{csgn}\left(d \right)\right) d}{x}\right)+18 b \,d^{2} e^{4} x^{6} \ln \left(\frac{2 \left(d +\sqrt{-e^{2} x^{2}+d^{2}}\, \mathrm{csgn}\left(d \right)\right) d}{x}\right)+24 c \,d^{4} e^{2} x^{6} \ln \left(\frac{2 \left(d +\sqrt{-e^{2} x^{2}+d^{2}}\, \mathrm{csgn}\left(d \right)\right) d}{x}\right)+15 \sqrt{-e^{2} x^{2}+d^{2}}\, a d \,e^{4} x^{4} \mathrm{csgn}\left(d \right)+18 \sqrt{-e^{2} x^{2}+d^{2}}\, b \,d^{3} e^{2} x^{4} \mathrm{csgn}\left(d \right)+24 \sqrt{-e^{2} x^{2}+d^{2}}\, c \,d^{5} x^{4} \mathrm{csgn}\left(d \right)+10 \sqrt{-e^{2} x^{2}+d^{2}}\, a \,d^{3} e^{2} x^{2} \mathrm{csgn}\left(d \right)+12 \sqrt{-e^{2} x^{2}+d^{2}}\, b \,d^{5} x^{2} \mathrm{csgn}\left(d \right)+8 \sqrt{-e^{2} x^{2}+d^{2}}\, a \,d^{5} \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{48 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{7} x^{6}}"," ",0,"-1/48*(-e*x+d)^(1/2)*(e*x+d)^(1/2)/d^7*(15*ln(2*(d+(-e^2*x^2+d^2)^(1/2)*csgn(d))*d/x)*x^6*a*e^6+18*ln(2*(d+(-e^2*x^2+d^2)^(1/2)*csgn(d))*d/x)*x^6*b*d^2*e^4+24*ln(2*(d+(-e^2*x^2+d^2)^(1/2)*csgn(d))*d/x)*x^6*c*d^4*e^2+15*(-e^2*x^2+d^2)^(1/2)*csgn(d)*d*x^4*a*e^4+18*(-e^2*x^2+d^2)^(1/2)*csgn(d)*d^3*x^4*b*e^2+24*(-e^2*x^2+d^2)^(1/2)*csgn(d)*d^5*x^4*c+10*csgn(d)*x^2*a*d^3*e^2*(-e^2*x^2+d^2)^(1/2)+12*csgn(d)*x^2*b*d^5*(-e^2*x^2+d^2)^(1/2)+8*csgn(d)*a*d^5*(-e^2*x^2+d^2)^(1/2))*csgn(d)/(-e^2*x^2+d^2)^(1/2)/x^6","C"
139,1,273,188,0.037000," ","int(x^2*(c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{-e x +d}\, \sqrt{e x +d}\, \left(8 \sqrt{-e^{2} x^{2}+d^{2}}\, c \,e^{5} x^{5} \mathrm{csgn}\left(e \right)+12 \sqrt{-e^{2} x^{2}+d^{2}}\, b \,e^{5} x^{3} \mathrm{csgn}\left(e \right)+10 \sqrt{-e^{2} x^{2}+d^{2}}\, c \,d^{2} e^{3} x^{3} \mathrm{csgn}\left(e \right)-24 a \,d^{2} e^{4} \arctan \left(\frac{e x \,\mathrm{csgn}\left(e \right)}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)+24 \sqrt{-e^{2} x^{2}+d^{2}}\, a \,e^{5} x \,\mathrm{csgn}\left(e \right)-18 b \,d^{4} e^{2} \arctan \left(\frac{e x \,\mathrm{csgn}\left(e \right)}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)+18 \sqrt{-e^{2} x^{2}+d^{2}}\, b \,d^{2} e^{3} x \,\mathrm{csgn}\left(e \right)-15 c \,d^{6} \arctan \left(\frac{e x \,\mathrm{csgn}\left(e \right)}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)+15 \sqrt{-e^{2} x^{2}+d^{2}}\, c \,d^{4} e x \,\mathrm{csgn}\left(e \right)\right) \mathrm{csgn}\left(e \right)}{48 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{7}}"," ",0,"-1/48*(-e*x+d)^(1/2)*(e*x+d)^(1/2)*(8*csgn(e)*x^5*c*e^5*(-e^2*x^2+d^2)^(1/2)+12*csgn(e)*x^3*b*e^5*(-e^2*x^2+d^2)^(1/2)+10*csgn(e)*x^3*c*d^2*e^3*(-e^2*x^2+d^2)^(1/2)+24*(-e^2*x^2+d^2)^(1/2)*csgn(e)*e^5*x*a+18*(-e^2*x^2+d^2)^(1/2)*csgn(e)*e^3*x*b*d^2+15*(-e^2*x^2+d^2)^(1/2)*csgn(e)*e*x*c*d^4-24*arctan(csgn(e)*e*x/(-e^2*x^2+d^2)^(1/2))*a*d^2*e^4-18*arctan(csgn(e)*e*x/(-e^2*x^2+d^2)^(1/2))*b*d^4*e^2-15*arctan(csgn(e)*e*x/(-e^2*x^2+d^2)^(1/2))*c*d^6)*csgn(e)/e^7/(-e^2*x^2+d^2)^(1/2)","C"
140,1,191,110,0.020000," ","int((c*x^4+b*x^2+a)/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{-e x +d}\, \sqrt{e x +d}\, \left(2 \sqrt{-e^{2} x^{2}+d^{2}}\, c \,e^{3} x^{3} \mathrm{csgn}\left(e \right)-8 a \,e^{4} \arctan \left(\frac{e x \,\mathrm{csgn}\left(e \right)}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)-4 b \,d^{2} e^{2} \arctan \left(\frac{e x \,\mathrm{csgn}\left(e \right)}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)+4 \sqrt{-e^{2} x^{2}+d^{2}}\, b \,e^{3} x \,\mathrm{csgn}\left(e \right)-3 c \,d^{4} \arctan \left(\frac{e x \,\mathrm{csgn}\left(e \right)}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)+3 \sqrt{-e^{2} x^{2}+d^{2}}\, c \,d^{2} e x \,\mathrm{csgn}\left(e \right)\right) \mathrm{csgn}\left(e \right)}{8 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{5}}"," ",0,"-1/8*(-e*x+d)^(1/2)*(e*x+d)^(1/2)*(2*csgn(e)*x^3*c*e^3*(-e^2*x^2+d^2)^(1/2)+4*(-e^2*x^2+d^2)^(1/2)*csgn(e)*e^3*x*b+3*(-e^2*x^2+d^2)^(1/2)*csgn(e)*e*x*c*d^2-8*arctan(1/(-e^2*x^2+d^2)^(1/2)*e*x*csgn(e))*a*e^4-4*arctan(1/(-e^2*x^2+d^2)^(1/2)*e*x*csgn(e))*b*d^2*e^2-3*arctan(1/(-e^2*x^2+d^2)^(1/2)*e*x*csgn(e))*c*d^4)*csgn(e)/e^5/(-e^2*x^2+d^2)^(1/2)","C"
141,1,148,88,0.023000," ","int((c*x^4+b*x^2+a)/x^2/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{-e x +d}\, \sqrt{e x +d}\, \left(-2 b \,d^{2} e^{2} x \arctan \left(\frac{e x \,\mathrm{csgn}\left(e \right)}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)-c \,d^{4} x \arctan \left(\frac{e x \,\mathrm{csgn}\left(e \right)}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)+\sqrt{-e^{2} x^{2}+d^{2}}\, c \,d^{2} e \,x^{2} \mathrm{csgn}\left(e \right)+2 \sqrt{-e^{2} x^{2}+d^{2}}\, a \,e^{3} \mathrm{csgn}\left(e \right)\right) \mathrm{csgn}\left(e \right)}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} e^{3} x}"," ",0,"-1/2*(-e*x+d)^(1/2)*(e*x+d)^(1/2)/d^2*(csgn(e)*x^2*c*d^2*e*(-e^2*x^2+d^2)^(1/2)-2*arctan(1/(-e^2*x^2+d^2)^(1/2)*e*x*csgn(e))*x*b*d^2*e^2-arctan(1/(-e^2*x^2+d^2)^(1/2)*e*x*csgn(e))*x*c*d^4+2*(-e^2*x^2+d^2)^(1/2)*csgn(e)*e^3*a)*csgn(e)/e^3/(-e^2*x^2+d^2)^(1/2)/x","C"
142,1,146,137,0.026000," ","int((c*x^4+b*x^2+a)/x^4/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{-e x +d}\, \sqrt{e x +d}\, \left(-3 c \,d^{4} x^{3} \arctan \left(\frac{e x \,\mathrm{csgn}\left(e \right)}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)+2 \sqrt{-e^{2} x^{2}+d^{2}}\, a \,e^{3} x^{2} \mathrm{csgn}\left(e \right)+3 \sqrt{-e^{2} x^{2}+d^{2}}\, b \,d^{2} e \,x^{2} \mathrm{csgn}\left(e \right)+\sqrt{-e^{2} x^{2}+d^{2}}\, a \,d^{2} e \,\mathrm{csgn}\left(e \right)\right) \mathrm{csgn}\left(e \right)}{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{4} e \,x^{3}}"," ",0,"-1/3*(-e*x+d)^(1/2)*(e*x+d)^(1/2)/d^4*(-3*arctan(1/(-e^2*x^2+d^2)^(1/2)*e*x*csgn(e))*x^3*c*d^4+2*(-e^2*x^2+d^2)^(1/2)*csgn(e)*e^3*x^2*a+3*(-e^2*x^2+d^2)^(1/2)*csgn(e)*e*x^2*b*d^2+a*(-e^2*x^2+d^2)^(1/2)*d^2*csgn(e)*e)*csgn(e)/(-e^2*x^2+d^2)^(1/2)/x^3/e","C"
143,1,82,142,0.005000," ","int((c*x^4+b*x^2+a)/x^6/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{e x +d}\, \sqrt{-e x +d}\, \left(8 a \,e^{4} x^{4}+10 b \,d^{2} e^{2} x^{4}+15 c \,d^{4} x^{4}+4 a \,d^{2} e^{2} x^{2}+5 b \,d^{4} x^{2}+3 a \,d^{4}\right)}{15 d^{6} x^{5}}"," ",0,"-1/15*(e*x+d)^(1/2)*(-e*x+d)^(1/2)*(8*a*e^4*x^4+10*b*d^2*e^2*x^4+15*c*d^4*x^4+4*a*d^2*e^2*x^2+5*b*d^4*x^2+3*a*d^4)/x^5/d^6","A"
144,1,118,202,0.007000," ","int((c*x^4+b*x^2+a)/x^8/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{e x +d}\, \sqrt{-e x +d}\, \left(48 a \,e^{6} x^{6}+56 b \,d^{2} e^{4} x^{6}+70 c \,d^{4} e^{2} x^{6}+24 a \,d^{2} e^{4} x^{4}+28 b \,d^{4} e^{2} x^{4}+35 c \,d^{6} x^{4}+18 a \,d^{4} e^{2} x^{2}+21 b \,d^{6} x^{2}+15 a \,d^{6}\right)}{105 d^{8} x^{7}}"," ",0,"-1/105*(e*x+d)^(1/2)*(-e*x+d)^(1/2)*(48*a*e^6*x^6+56*b*d^2*e^4*x^6+70*c*d^4*e^2*x^6+24*a*d^2*e^4*x^4+28*b*d^4*e^2*x^4+35*c*d^6*x^4+18*a*d^4*e^2*x^2+21*b*d^6*x^2+15*a*d^6)/x^7/d^8","A"
145,1,154,262,0.007000," ","int((c*x^4+b*x^2+a)/x^10/(-e*x+d)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{e x +d}\, \sqrt{-e x +d}\, \left(128 a \,e^{8} x^{8}+144 b \,d^{2} e^{6} x^{8}+168 c \,d^{4} e^{4} x^{8}+64 a \,d^{2} e^{6} x^{6}+72 b \,d^{4} e^{4} x^{6}+84 c \,d^{6} e^{2} x^{6}+48 a \,d^{4} e^{4} x^{4}+54 b \,d^{6} e^{2} x^{4}+63 c \,d^{8} x^{4}+40 a \,d^{6} e^{2} x^{2}+45 b \,d^{8} x^{2}+35 a \,d^{8}\right)}{315 d^{10} x^{9}}"," ",0,"-1/315*(e*x+d)^(1/2)*(-e*x+d)^(1/2)*(128*a*e^8*x^8+144*b*d^2*e^6*x^8+168*c*d^4*e^4*x^8+64*a*d^2*e^6*x^6+72*b*d^4*e^4*x^6+84*c*d^6*e^2*x^6+48*a*d^4*e^4*x^4+54*b*d^6*e^2*x^4+63*c*d^8*x^4+40*a*d^6*e^2*x^2+45*b*d^8*x^2+35*a*d^8)/x^9/d^10","A"