1,1,20,19,0.000000," ","int(x^2*(c*x^4+b*x^3+a*x^2),x)","\frac{1}{7} c \,x^{7}+\frac{1}{6} b \,x^{6}+\frac{1}{5} a \,x^{5}"," ",0,"1/5*a*x^5+1/6*b*x^6+1/7*c*x^7","A"
2,1,20,19,0.000000," ","int(x*(c*x^4+b*x^3+a*x^2),x)","\frac{1}{6} c \,x^{6}+\frac{1}{5} b \,x^{5}+\frac{1}{4} a \,x^{4}"," ",0,"1/4*a*x^4+1/5*b*x^5+1/6*c*x^6","A"
3,1,20,19,0.002000," ","int(c*x^4+b*x^3+a*x^2,x)","\frac{1}{5} c \,x^{5}+\frac{1}{4} b \,x^{4}+\frac{1}{3} a \,x^{3}"," ",0,"1/3*a*x^3+1/4*b*x^4+1/5*c*x^5","A"
4,1,20,19,0.001000," ","int((c*x^4+b*x^3+a*x^2)/x,x)","\frac{1}{4} c \,x^{4}+\frac{1}{3} b \,x^{3}+\frac{1}{2} a \,x^{2}"," ",0,"1/2*a*x^2+1/3*b*x^3+1/4*c*x^4","A"
5,1,17,16,0.001000," ","int((c*x^4+b*x^3+a*x^2)/x^2,x)","\frac{1}{3} c \,x^{3}+\frac{1}{2} b \,x^{2}+a x"," ",0,"a*x+1/2*b*x^2+1/3*c*x^3","A"
6,1,45,44,0.000000," ","int(x^2*(c*x^4+b*x^3+a*x^2)^2,x)","\frac{c^{2} x^{11}}{11}+\frac{b c \,x^{10}}{5}+\frac{a b \,x^{8}}{4}+\frac{a^{2} x^{7}}{7}+\frac{\left(2 a c +b^{2}\right) x^{9}}{9}"," ",0,"1/7*a^2*x^7+1/4*a*b*x^8+1/9*(2*a*c+b^2)*x^9+1/5*b*c*x^10+1/11*c^2*x^11","A"
7,1,45,44,0.001000," ","int(x*(c*x^4+b*x^3+a*x^2)^2,x)","\frac{c^{2} x^{10}}{10}+\frac{2 b c \,x^{9}}{9}+\frac{2 a b \,x^{7}}{7}+\frac{a^{2} x^{6}}{6}+\frac{\left(2 a c +b^{2}\right) x^{8}}{8}"," ",0,"1/6*a^2*x^6+2/7*a*b*x^7+1/8*(2*a*c+b^2)*x^8+2/9*b*c*x^9+1/10*c^2*x^10","A"
8,1,45,44,0.000000," ","int((c*x^4+b*x^3+a*x^2)^2,x)","\frac{c^{2} x^{9}}{9}+\frac{b c \,x^{8}}{4}+\frac{a b \,x^{6}}{3}+\frac{a^{2} x^{5}}{5}+\frac{\left(2 a c +b^{2}\right) x^{7}}{7}"," ",0,"1/5*a^2*x^5+1/3*a*b*x^6+1/7*(2*a*c+b^2)*x^7+1/4*b*c*x^8+1/9*c^2*x^9","A"
9,1,45,44,0.002000," ","int((c*x^4+b*x^3+a*x^2)^2/x,x)","\frac{c^{2} x^{8}}{8}+\frac{2 b c \,x^{7}}{7}+\frac{2 a b \,x^{5}}{5}+\frac{a^{2} x^{4}}{4}+\frac{\left(2 a c +b^{2}\right) x^{6}}{6}"," ",0,"1/4*a^2*x^4+2/5*a*b*x^5+1/6*(2*a*c+b^2)*x^6+2/7*b*c*x^7+1/8*c^2*x^8","A"
10,1,45,44,0.002000," ","int((c*x^4+b*x^3+a*x^2)^2/x^2,x)","\frac{c^{2} x^{7}}{7}+\frac{b c \,x^{6}}{3}+\frac{a b \,x^{4}}{2}+\frac{a^{2} x^{3}}{3}+\frac{\left(2 a c +b^{2}\right) x^{5}}{5}"," ",0,"1/3*a^2*x^3+1/2*a*b*x^4+1/5*(2*a*c+b^2)*x^5+1/3*b*c*x^6+1/7*c^2*x^7","A"
11,1,132,81,0.005000," ","int(x^5/(c*x^4+b*x^3+a*x^2),x)","\frac{3 a b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{2}}-\frac{b^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{3}}+\frac{x^{2}}{2 c}-\frac{a \ln \left(c \,x^{2}+b x +a \right)}{2 c^{2}}+\frac{b^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 c^{3}}-\frac{b x}{c^{2}}"," ",0,"1/2/c*x^2-b/c^2*x-1/2/c^2*ln(c*x^2+b*x+a)*a+1/2/c^3*ln(c*x^2+b*x+a)*b^2+3/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b-1/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3","A"
12,1,101,64,0.003000," ","int(x^4/(c*x^4+b*x^3+a*x^2),x)","-\frac{2 a \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{b^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{2}}-\frac{b \ln \left(c \,x^{2}+b x +a \right)}{2 c^{2}}+\frac{x}{c}"," ",0,"1/c*x-1/2*b/c^2*ln(c*x^2+b*x+a)-2/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a+1/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2","A"
13,1,56,50,0.003000," ","int(x^3/(c*x^4+b*x^3+a*x^2),x)","-\frac{b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{\ln \left(c \,x^{2}+b x +a \right)}{2 c}"," ",0,"1/2/c*ln(c*x^2+b*x+a)-b/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
14,1,35,30,0.001000," ","int(x^2/(c*x^4+b*x^3+a*x^2),x)","\frac{2 \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}"," ",0,"2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
15,1,62,56,0.007000," ","int(x/(c*x^4+b*x^3+a*x^2),x)","-\frac{b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a}+\frac{\ln \left(x \right)}{a}-\frac{\ln \left(c \,x^{2}+b x +a \right)}{2 a}"," ",0,"1/a*ln(x)-1/2/a*ln(c*x^2+b*x+a)-1/a*b/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
16,1,112,75,0.007000," ","int(1/(c*x^4+b*x^3+a*x^2),x)","-\frac{2 c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a}+\frac{b^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{2}}-\frac{b \ln \left(x \right)}{a^{2}}+\frac{b \ln \left(c \,x^{2}+b x +a \right)}{2 a^{2}}-\frac{1}{a x}"," ",0,"-1/a/x-1/a^2*b*ln(x)+1/2/a^2*b*ln(c*x^2+b*x+a)-2/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c+1/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2","A"
17,1,150,96,0.007000," ","int(1/x/(c*x^4+b*x^3+a*x^2),x)","\frac{3 b c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{2}}-\frac{b^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{3}}-\frac{c \ln \left(x \right)}{a^{2}}+\frac{c \ln \left(c \,x^{2}+b x +a \right)}{2 a^{2}}+\frac{b^{2} \ln \left(x \right)}{a^{3}}-\frac{b^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 a^{3}}+\frac{b}{a^{2} x}-\frac{1}{2 a \,x^{2}}"," ",0,"-1/2/a/x^2-1/a^2*ln(x)*c+1/a^3*ln(x)*b^2+1/a^2*b/x+1/2/a^2*c*ln(c*x^2+b*x+a)-1/2/a^3*ln(c*x^2+b*x+a)*b^2+3/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c-1/a^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3","A"
18,1,214,127,0.010000," ","int(1/x^2/(c*x^4+b*x^3+a*x^2),x)","\frac{2 c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{2}}-\frac{4 b^{2} c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{3}}+\frac{b^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{4}}+\frac{2 b c \ln \left(x \right)}{a^{3}}-\frac{b c \ln \left(c \,x^{2}+b x +a \right)}{a^{3}}-\frac{b^{3} \ln \left(x \right)}{a^{4}}+\frac{b^{3} \ln \left(c \,x^{2}+b x +a \right)}{2 a^{4}}+\frac{c}{a^{2} x}-\frac{b^{2}}{a^{3} x}+\frac{b}{2 a^{2} x^{2}}-\frac{1}{3 a \,x^{3}}"," ",0,"-1/3/a/x^3+1/a^2/x*c-1/a^3/x*b^2+2*b/a^3*ln(x)*c-b^3/a^4*ln(x)+1/2/a^2*b/x^2-1/a^3*c*ln(c*x^2+b*x+a)*b+1/2/a^4*ln(c*x^2+b*x+a)*b^3+2/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2-4/a^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*c+1/a^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4","A"
19,1,352,146,0.010000," ","int(x^8/(c*x^4+b*x^3+a*x^2)^2,x)","\frac{2 a^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c}-\frac{12 a^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}-\frac{4 a \,b^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{12 a \,b^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}+\frac{b^{4} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{2 b^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{3}}-\frac{3 a^{2} b}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{a \,b^{3}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{4 a b \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{2}}+\frac{b^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{3}}+\frac{x}{c^{2}}"," ",0,"x/c^2+2/c/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a^2-4/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a*b^2+1/c^3/(c*x^2+b*x+a)/(4*a*c-b^2)*x*b^4-3/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*a^2*b+1/c^3/(c*x^2+b*x+a)/(4*a*c-b^2)*a*b^3-4/c^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*a*b+1/c^3/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^3-12/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2+12/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2-2/c^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4","B"
20,1,209,108,0.009000," ","int(x^7/(c*x^4+b*x^3+a*x^2)^2,x)","-\frac{6 a b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}+\frac{b^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}+\frac{2 a \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c}-\frac{b^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(4 a c -b^{2}\right) c^{2}}+\frac{\frac{\left(3 a c -b^{2}\right) b x}{\left(4 a c -b^{2}\right) c^{2}}+\frac{\left(2 a c -b^{2}\right) a}{\left(4 a c -b^{2}\right) c^{2}}}{c \,x^{2}+b x +a}"," ",0,"((3*a*c-b^2)/(4*a*c-b^2)*b/c^2*x+(2*a*c-b^2)/(4*a*c-b^2)*a/c^2)/(c*x^2+b*x+a)+2/c/(4*a*c-b^2)*ln(c*x^2+b*x+a)*a-1/2/c^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^2-6/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b+1/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3","A"
21,1,97,63,0.007000," ","int(x^6/(c*x^4+b*x^3+a*x^2)^2,x)","\frac{4 a \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{\frac{a b}{\left(4 a c -b^{2}\right) c}-\frac{\left(2 a c -b^{2}\right) x}{\left(4 a c -b^{2}\right) c}}{c \,x^{2}+b x +a}"," ",0,"(-(2*a*c-b^2)/(4*a*c-b^2)/c*x+1/(4*a*c-b^2)*a*b/c)/(c*x^2+b*x+a)+4*a/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
22,1,70,62,0.003000," ","int(x^5/(c*x^4+b*x^3+a*x^2)^2,x)","-\frac{2 b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{-b x -2 a}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)}"," ",0,"(-b*x-2*a)/(4*a*c-b^2)/(c*x^2+b*x+a)-2*b/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
23,1,68,63,0.004000," ","int(x^4/(c*x^4+b*x^3+a*x^2)^2,x)","\frac{4 c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 c x +b}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)}"," ",0,"(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)+4*c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
24,1,237,102,0.014000," ","int(x^3/(c*x^4+b*x^3+a*x^2)^2,x)","-\frac{b c x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a}-\frac{6 b c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a}+\frac{b^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}-\frac{b^{2}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a}-\frac{2 c \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a}+\frac{b^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(4 a c -b^{2}\right) a^{2}}+\frac{2 c}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{\ln \left(x \right)}{a^{2}}"," ",0,"1/a^2*ln(x)-1/a/(c*x^2+b*x+a)*b*c/(4*a*c-b^2)*x+2/(c*x^2+b*x+a)/(4*a*c-b^2)*c-1/a/(c*x^2+b*x+a)/(4*a*c-b^2)*b^2-2/a/(4*a*c-b^2)*c*ln(c*x^2+b*x+a)+1/2/a^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^2-6/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c+1/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3","B"
25,1,328,144,0.015000," ","int(x^2/(c*x^4+b*x^3+a*x^2)^2,x)","-\frac{2 c^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a}-\frac{12 c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a}+\frac{b^{2} c x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{12 b^{2} c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}-\frac{2 b^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{3}}-\frac{3 b c}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{3}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{4 b c \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a^{2}}-\frac{b^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a^{3}}-\frac{2 b \ln \left(x \right)}{a^{3}}-\frac{1}{a^{2} x}"," ",0,"-1/a^2/x-2/a^3*b*ln(x)-2/a/(c*x^2+b*x+a)*c^2/(4*a*c-b^2)*x+1/a^2/(c*x^2+b*x+a)*c/(4*a*c-b^2)*x*b^2-3/a/(c*x^2+b*x+a)*b/(4*a*c-b^2)*c+1/a^2/(c*x^2+b*x+a)*b^3/(4*a*c-b^2)+4/a^2/(4*a*c-b^2)*c*ln(c*x^2+b*x+a)*b-1/a^3/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^3-12/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2+12/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*c-2/a^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4","B"
26,1,418,194,0.016000," ","int(x/(c*x^4+b*x^3+a*x^2)^2,x)","\frac{3 b \,c^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{30 b \,c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}-\frac{b^{3} c x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{3}}-\frac{20 b^{3} c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{3}}+\frac{3 b^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{4}}-\frac{2 c^{2}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a}+\frac{4 b^{2} c}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{4 c^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a^{2}}-\frac{b^{4}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{3}}-\frac{7 b^{2} c \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a^{3}}+\frac{3 b^{4} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(4 a c -b^{2}\right) a^{4}}-\frac{2 c \ln \left(x \right)}{a^{3}}+\frac{3 b^{2} \ln \left(x \right)}{a^{4}}+\frac{2 b}{a^{3} x}-\frac{1}{2 a^{2} x^{2}}"," ",0,"-1/2/a^2/x^2-2/a^3*ln(x)*c+3/a^4*ln(x)*b^2+2/a^3*b/x+3/a^2/(c*x^2+b*x+a)*b*c^2/(4*a*c-b^2)*x-1/a^3/(c*x^2+b*x+a)*b^3*c/(4*a*c-b^2)*x-2/a/(c*x^2+b*x+a)/(4*a*c-b^2)*c^2+4/a^2/(c*x^2+b*x+a)/(4*a*c-b^2)*b^2*c-1/a^3/(c*x^2+b*x+a)/(4*a*c-b^2)*b^4+4/a^2/(4*a*c-b^2)*c^2*ln(c*x^2+b*x+a)-7/a^3/(4*a*c-b^2)*c*ln(c*x^2+b*x+a)*b^2+3/2/a^4/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^4+30/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c^2-20/a^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*c+3/a^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^5","B"
27,1,515,246,0.017000," ","int(1/(c*x^4+b*x^3+a*x^2)^2,x)","\frac{2 c^{3} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{20 c^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}-\frac{4 b^{2} c^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{3}}-\frac{60 b^{2} c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{3}}+\frac{b^{4} c x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{4}}+\frac{30 b^{4} c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{4}}-\frac{4 b^{6} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{5}}+\frac{5 b \,c^{2}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{5 b^{3} c}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{3}}-\frac{12 b \,c^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a^{3}}+\frac{b^{5}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{4}}+\frac{11 b^{3} c \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a^{4}}-\frac{2 b^{5} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a^{5}}+\frac{6 b c \ln \left(x \right)}{a^{4}}-\frac{4 b^{3} \ln \left(x \right)}{a^{5}}+\frac{2 c}{a^{3} x}-\frac{3 b^{2}}{a^{4} x}+\frac{b}{a^{3} x^{2}}-\frac{1}{3 a^{2} x^{3}}"," ",0,"-1/3/a^2/x^3+2/a^3/x*c-3/a^4/x*b^2+1/a^3*b/x^2+6*b/a^4*ln(x)*c-4*b^3/a^5*ln(x)+2/a^2/(c*x^2+b*x+a)*c^3/(4*a*c-b^2)*x-4/a^3/(c*x^2+b*x+a)*c^2/(4*a*c-b^2)*x*b^2+1/a^4/(c*x^2+b*x+a)*c/(4*a*c-b^2)*x*b^4+5/a^2/(c*x^2+b*x+a)*b/(4*a*c-b^2)*c^2-5/a^3/(c*x^2+b*x+a)*b^3/(4*a*c-b^2)*c+1/a^4/(c*x^2+b*x+a)*b^5/(4*a*c-b^2)-12/a^3/(4*a*c-b^2)*c^2*ln(c*x^2+b*x+a)*b+11/a^4/(4*a*c-b^2)*c*ln(c*x^2+b*x+a)*b^3-2/a^5/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^5+20/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^3-60/a^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*c^2+30/a^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4*c-4/a^5/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^6","B"
28,1,619,306,0.020000," ","int(1/x/(c*x^4+b*x^3+a*x^2)^2,x)","-\frac{5 b \,c^{3} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{3}}-\frac{70 b \,c^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{3}}+\frac{5 b^{3} c^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{4}}+\frac{105 b^{3} c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{4}}-\frac{b^{5} c x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{5}}-\frac{42 b^{5} c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{5}}+\frac{5 b^{7} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{6}}+\frac{2 c^{3}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{9 b^{2} c^{2}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{3}}-\frac{6 c^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a^{3}}+\frac{6 b^{4} c}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{4}}+\frac{51 b^{2} c^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(4 a c -b^{2}\right) a^{4}}-\frac{b^{6}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{5}}-\frac{16 b^{4} c \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a^{5}}+\frac{5 b^{6} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(4 a c -b^{2}\right) a^{6}}+\frac{3 c^{2} \ln \left(x \right)}{a^{4}}-\frac{12 b^{2} c \ln \left(x \right)}{a^{5}}+\frac{5 b^{4} \ln \left(x \right)}{a^{6}}-\frac{6 b c}{a^{4} x}+\frac{4 b^{3}}{a^{5} x}+\frac{c}{a^{3} x^{2}}-\frac{3 b^{2}}{2 a^{4} x^{2}}+\frac{2 b}{3 a^{3} x^{3}}-\frac{1}{4 a^{2} x^{4}}"," ",0,"-1/4/a^2/x^4+1/a^3/x^2*c-3/2/a^4/x^2*b^2+3/a^4*ln(x)*c^2-12/a^5*ln(x)*b^2*c+5/a^6*ln(x)*b^4+2/3/a^3*b/x^3-6*b/a^4/x*c+4*b^3/a^5/x-5/a^3/(c*x^2+b*x+a)*b*c^3/(4*a*c-b^2)*x+5/a^4/(c*x^2+b*x+a)*b^3*c^2/(4*a*c-b^2)*x-1/a^5/(c*x^2+b*x+a)*b^5*c/(4*a*c-b^2)*x+2/a^2/(c*x^2+b*x+a)/(4*a*c-b^2)*c^3-9/a^3/(c*x^2+b*x+a)/(4*a*c-b^2)*b^2*c^2+6/a^4/(c*x^2+b*x+a)/(4*a*c-b^2)*b^4*c-1/a^5/(c*x^2+b*x+a)/(4*a*c-b^2)*b^6-6/a^3/(4*a*c-b^2)*c^3*ln(c*x^2+b*x+a)+51/2/a^4/(4*a*c-b^2)*c^2*ln(c*x^2+b*x+a)*b^2-16/a^5/(4*a*c-b^2)*c*ln(c*x^2+b*x+a)*b^4+5/2/a^6/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^6-70/a^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c^3+105/a^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*c^2-42/a^5/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^5*c+5/a^6/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^7","B"
29,1,310,227,0.009000," ","int(x^2*(c*x^4+b*x^3+a*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, \left(720 a^{2} b \,c^{3} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-600 a \,b^{3} c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+105 b^{5} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+720 \sqrt{c \,x^{2}+b x +a}\, a b \,c^{\frac{7}{2}} x -420 \sqrt{c \,x^{2}+b x +a}\, b^{3} c^{\frac{5}{2}} x +768 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{\frac{9}{2}} x^{2}+360 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} c^{\frac{5}{2}}-210 \sqrt{c \,x^{2}+b x +a}\, b^{4} c^{\frac{3}{2}}-672 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,c^{\frac{7}{2}} x -512 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,c^{\frac{7}{2}}+560 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} c^{\frac{5}{2}}\right)}{3840 \sqrt{c \,x^{2}+b x +a}\, c^{\frac{11}{2}} x}"," ",0,"1/3840*(c*x^4+b*x^3+a*x^2)^(1/2)*(768*x^2*(c*x^2+b*x+a)^(3/2)*c^(9/2)-672*c^(7/2)*(c*x^2+b*x+a)^(3/2)*x*b-512*c^(7/2)*(c*x^2+b*x+a)^(3/2)*a+560*c^(5/2)*(c*x^2+b*x+a)^(3/2)*b^2+720*c^(7/2)*(c*x^2+b*x+a)^(1/2)*x*a*b-420*c^(5/2)*(c*x^2+b*x+a)^(1/2)*x*b^3+360*c^(5/2)*(c*x^2+b*x+a)^(1/2)*a*b^2-210*c^(3/2)*(c*x^2+b*x+a)^(1/2)*b^4+720*ln(1/2*(2*(c*x^2+b*x+a)^(1/2)*c^(1/2)+2*c*x+b)/c^(1/2))*a^2*b*c^3-600*ln(1/2*(2*(c*x^2+b*x+a)^(1/2)*c^(1/2)+2*c*x+b)/c^(1/2))*a*b^3*c^2+105*ln(1/2*(2*(c*x^2+b*x+a)^(1/2)*c^(1/2)+2*c*x+b)/c^(1/2))*b^5*c)/x/(c*x^2+b*x+a)^(1/2)/c^(11/2)","A"
30,1,265,179,0.009000," ","int(x*(c*x^4+b*x^3+a*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, \left(-48 a^{2} c^{3} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+72 a \,b^{2} c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-15 b^{4} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-48 \sqrt{c \,x^{2}+b x +a}\, a \,c^{\frac{7}{2}} x +60 \sqrt{c \,x^{2}+b x +a}\, b^{2} c^{\frac{5}{2}} x -24 \sqrt{c \,x^{2}+b x +a}\, a b \,c^{\frac{5}{2}}+30 \sqrt{c \,x^{2}+b x +a}\, b^{3} c^{\frac{3}{2}}+96 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{\frac{7}{2}} x -80 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,c^{\frac{5}{2}}\right)}{384 \sqrt{c \,x^{2}+b x +a}\, c^{\frac{9}{2}} x}"," ",0,"1/384*(c*x^4+b*x^3+a*x^2)^(1/2)*(96*x*(c*x^2+b*x+a)^(3/2)*c^(7/2)-80*c^(5/2)*(c*x^2+b*x+a)^(3/2)*b-48*c^(7/2)*(c*x^2+b*x+a)^(1/2)*x*a+60*c^(5/2)*(c*x^2+b*x+a)^(1/2)*x*b^2-24*c^(5/2)*(c*x^2+b*x+a)^(1/2)*a*b+30*c^(3/2)*(c*x^2+b*x+a)^(1/2)*b^3-48*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a^2*c^3+72*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a*b^2*c^2-15*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*b^4*c)/x/(c*x^2+b*x+a)^(1/2)/c^(9/2)","A"
31,1,167,141,0.008000," ","int((c*x^4+b*x^3+a*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, \left(-12 a b \,c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+3 b^{3} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-12 \sqrt{c \,x^{2}+b x +a}\, b \,c^{\frac{5}{2}} x -6 \sqrt{c \,x^{2}+b x +a}\, b^{2} c^{\frac{3}{2}}+16 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{\frac{5}{2}}\right)}{48 \sqrt{c \,x^{2}+b x +a}\, c^{\frac{7}{2}} x}"," ",0,"1/48*(c*x^4+b*x^3+a*x^2)^(1/2)*(16*(c*x^2+b*x+a)^(3/2)*c^(5/2)-12*c^(5/2)*(c*x^2+b*x+a)^(1/2)*x*b-6*c^(3/2)*(c*x^2+b*x+a)^(1/2)*b^2-12*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a*b*c^2+3*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*b^3*c)/x/(c*x^2+b*x+a)^(1/2)/c^(7/2)","A"
32,1,146,101,0.005000," ","int((c*x^4+b*x^3+a*x^2)^(1/2)/x,x)","\frac{\sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, \left(4 a \,c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-b^{2} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+4 \sqrt{c \,x^{2}+b x +a}\, c^{\frac{5}{2}} x +2 \sqrt{c \,x^{2}+b x +a}\, b \,c^{\frac{3}{2}}\right)}{8 \sqrt{c \,x^{2}+b x +a}\, c^{\frac{5}{2}} x}"," ",0,"1/8*(c*x^4+b*x^3+a*x^2)^(1/2)*(4*(c*x^2+b*x+a)^(1/2)*c^(5/2)*x+2*(c*x^2+b*x+a)^(1/2)*c^(3/2)*b+4*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a*c^2-ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*b^2*c)/(c*x^2+b*x+a)^(1/2)/c^(5/2)/x","A"
33,1,126,145,0.006000," ","int((c*x^4+b*x^3+a*x^2)^(1/2)/x^2,x)","-\frac{\sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, \left(2 \sqrt{a}\, \sqrt{c}\, \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-b \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}\right)}{2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}\, x}"," ",0,"-1/2*(c*x^4+b*x^3+a*x^2)^(1/2)*(2*a^(1/2)*ln((2*a+b*x+2*a^(1/2)*(c*x^2+b*x+a)^(1/2))/x)*c^(1/2)-2*(c*x^2+b*x+a)^(1/2)*c^(1/2)-b*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2)))/x/(c*x^2+b*x+a)^(1/2)/c^(1/2)","A"
34,1,173,145,0.006000," ","int((c*x^4+b*x^3+a*x^2)^(1/2)/x^3,x)","-\frac{\sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, \left(-2 a \,c^{2} x \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+\sqrt{a}\, b \,c^{\frac{3}{2}} x \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-2 \sqrt{c \,x^{2}+b x +a}\, c^{\frac{5}{2}} x^{2}-2 \sqrt{c \,x^{2}+b x +a}\, b \,c^{\frac{3}{2}} x +2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{\frac{3}{2}}\right)}{2 \sqrt{c \,x^{2}+b x +a}\, a \,c^{\frac{3}{2}} x^{2}}"," ",0,"-1/2*(c*x^4+b*x^3+a*x^2)^(1/2)*(-2*(c*x^2+b*x+a)^(1/2)*c^(5/2)*x^2+c^(3/2)*a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x*b+2*(c*x^2+b*x+a)^(3/2)*c^(3/2)-2*(c*x^2+b*x+a)^(1/2)*c^(3/2)*x*b-2*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*x*a*c^2)/x^2/(c*x^2+b*x+a)^(1/2)/a/c^(3/2)","A"
35,1,207,96,0.006000," ","int((c*x^4+b*x^3+a*x^2)^(1/2)/x^4,x)","-\frac{\sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, \left(4 a^{\frac{3}{2}} c \,x^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-\sqrt{a}\, b^{2} x^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+2 \sqrt{c \,x^{2}+b x +a}\, b c \,x^{3}-4 \sqrt{c \,x^{2}+b x +a}\, a c \,x^{2}+2 \sqrt{c \,x^{2}+b x +a}\, b^{2} x^{2}-2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b x +4 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \right)}{8 \sqrt{c \,x^{2}+b x +a}\, a^{2} x^{3}}"," ",0,"-1/8*(c*x^4+b*x^3+a*x^2)^(1/2)*(4*c*a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^2+2*c*(c*x^2+b*x+a)^(1/2)*x^3*b-4*c*(c*x^2+b*x+a)^(1/2)*x^2*a-a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^2*b^2-2*(c*x^2+b*x+a)^(3/2)*x*b+2*(c*x^2+b*x+a)^(1/2)*x^2*b^2+4*(c*x^2+b*x+a)^(3/2)*a)/x^3/(c*x^2+b*x+a)^(1/2)/a^2","B"
36,1,234,133,0.008000," ","int((c*x^4+b*x^3+a*x^2)^(1/2)/x^5,x)","\frac{\sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, \left(12 a^{\frac{3}{2}} b c \,x^{3} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-3 \sqrt{a}\, b^{3} x^{3} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+6 \sqrt{c \,x^{2}+b x +a}\, b^{2} c \,x^{4}-12 \sqrt{c \,x^{2}+b x +a}\, a b c \,x^{3}+6 \sqrt{c \,x^{2}+b x +a}\, b^{3} x^{3}-6 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} x^{2}+12 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b x -16 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2}\right)}{48 \sqrt{c \,x^{2}+b x +a}\, a^{3} x^{4}}"," ",0,"1/48*(c*x^4+b*x^3+a*x^2)^(1/2)*(12*c*a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^3*b+6*c*(c*x^2+b*x+a)^(1/2)*x^4*b^2-12*c*(c*x^2+b*x+a)^(1/2)*x^3*a*b-3*a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^3*b^3-6*(c*x^2+b*x+a)^(3/2)*x^2*b^2+6*(c*x^2+b*x+a)^(1/2)*x^3*b^3+12*(c*x^2+b*x+a)^(3/2)*x*a*b-16*(c*x^2+b*x+a)^(3/2)*a^2)/x^4/(c*x^2+b*x+a)^(1/2)/a^3","A"
37,1,387,179,0.011000," ","int((c*x^4+b*x^3+a*x^2)^(1/2)/x^6,x)","\frac{\sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, \left(48 a^{\frac{5}{2}} c^{2} x^{4} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-72 a^{\frac{3}{2}} b^{2} c \,x^{4} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+15 \sqrt{a}\, b^{4} x^{4} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+24 \sqrt{c \,x^{2}+b x +a}\, a b \,c^{2} x^{5}-30 \sqrt{c \,x^{2}+b x +a}\, b^{3} c \,x^{5}-48 \sqrt{c \,x^{2}+b x +a}\, a^{2} c^{2} x^{4}+84 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} c \,x^{4}-30 \sqrt{c \,x^{2}+b x +a}\, b^{4} x^{4}-24 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b c \,x^{3}+30 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} x^{3}+48 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} c \,x^{2}-60 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} x^{2}+80 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} b x -96 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{3}\right)}{384 \sqrt{c \,x^{2}+b x +a}\, a^{4} x^{5}}"," ",0,"1/384*(c*x^4+b*x^3+a*x^2)^(1/2)*(48*c^2*a^(5/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^4+24*c^2*(c*x^2+b*x+a)^(1/2)*x^5*a*b-72*c*a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^4*b^2-48*c^2*(c*x^2+b*x+a)^(1/2)*x^4*a^2-30*c*(c*x^2+b*x+a)^(1/2)*x^5*b^3-24*c*(c*x^2+b*x+a)^(3/2)*x^3*a*b+84*c*(c*x^2+b*x+a)^(1/2)*x^4*a*b^2+15*a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^4*b^4+48*c*(c*x^2+b*x+a)^(3/2)*x^2*a^2+30*(c*x^2+b*x+a)^(3/2)*x^3*b^3-30*(c*x^2+b*x+a)^(1/2)*x^4*b^4-60*(c*x^2+b*x+a)^(3/2)*x^2*a*b^2+80*(c*x^2+b*x+a)^(3/2)*x*a^2*b-96*(c*x^2+b*x+a)^(3/2)*a^3)/x^5/(c*x^2+b*x+a)^(1/2)/a^4","B"
38,1,649,384,0.010000," ","int(x*(c*x^4+b*x^3+a*x^2)^(3/2),x)","\frac{\left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(26880 a^{4} c^{5} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-134400 a^{3} b^{2} c^{4} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+117600 a^{2} b^{4} c^{3} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-35280 a \,b^{6} c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+3465 b^{8} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+26880 \sqrt{c \,x^{2}+b x +a}\, a^{3} c^{\frac{11}{2}} x -127680 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} c^{\frac{9}{2}} x +85680 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} c^{\frac{7}{2}} x -13860 \sqrt{c \,x^{2}+b x +a}\, b^{6} c^{\frac{5}{2}} x +143360 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} c^{\frac{13}{2}} x^{3}+13440 \sqrt{c \,x^{2}+b x +a}\, a^{3} b \,c^{\frac{9}{2}}-63840 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{3} c^{\frac{7}{2}}+17920 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} c^{\frac{11}{2}} x +42840 \sqrt{c \,x^{2}+b x +a}\, a \,b^{5} c^{\frac{5}{2}}-80640 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} c^{\frac{9}{2}} x -6930 \sqrt{c \,x^{2}+b x +a}\, b^{7} c^{\frac{3}{2}}+36960 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} c^{\frac{7}{2}} x -112640 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b \,c^{\frac{11}{2}} x^{2}+8960 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} b \,c^{\frac{9}{2}}-40320 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{3} c^{\frac{7}{2}}-71680 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,c^{\frac{11}{2}} x +18480 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{5} c^{\frac{5}{2}}+84480 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{2} c^{\frac{9}{2}} x +95232 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a b \,c^{\frac{9}{2}}-59136 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{3} c^{\frac{7}{2}}\right)}{1146880 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{\frac{15}{2}} x^{3}}"," ",0,"1/1146880*(c*x^4+b*x^3+a*x^2)^(3/2)*(26880*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a^4*c^5+3465*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*b^8*c+143360*x^3*(c*x^2+b*x+a)^(5/2)*c^(13/2)-59136*(c*x^2+b*x+a)^(5/2)*c^(7/2)*b^3+18480*(c*x^2+b*x+a)^(3/2)*c^(5/2)*b^5-6930*(c*x^2+b*x+a)^(1/2)*c^(3/2)*b^7+42840*(c*x^2+b*x+a)^(1/2)*c^(5/2)*a*b^5+8960*(c*x^2+b*x+a)^(3/2)*c^(9/2)*a^2*b-40320*(c*x^2+b*x+a)^(3/2)*c^(7/2)*a*b^3-134400*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a^3*b^2*c^4+117600*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a^2*b^4*c^3-35280*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a*b^6*c^2-13860*(c*x^2+b*x+a)^(1/2)*c^(5/2)*x*b^6+13440*(c*x^2+b*x+a)^(1/2)*c^(9/2)*a^3*b-63840*(c*x^2+b*x+a)^(1/2)*c^(7/2)*a^2*b^3-112640*(c*x^2+b*x+a)^(5/2)*c^(11/2)*x^2*b-71680*(c*x^2+b*x+a)^(5/2)*c^(11/2)*x*a+84480*(c*x^2+b*x+a)^(5/2)*c^(9/2)*x*b^2+95232*(c*x^2+b*x+a)^(5/2)*c^(9/2)*a*b+17920*(c*x^2+b*x+a)^(3/2)*c^(11/2)*x*a^2+36960*(c*x^2+b*x+a)^(3/2)*c^(7/2)*x*b^4+26880*(c*x^2+b*x+a)^(1/2)*c^(11/2)*x*a^3-80640*(c*x^2+b*x+a)^(3/2)*c^(9/2)*x*a*b^2-127680*(c*x^2+b*x+a)^(1/2)*c^(9/2)*x*a^2*b^2+85680*(c*x^2+b*x+a)^(1/2)*c^(7/2)*x*a*b^4)/x^3/(c*x^2+b*x+a)^(3/2)/c^(15/2)","A"
39,1,479,326,0.010000," ","int((c*x^4+b*x^3+a*x^2)^(3/2),x)","\frac{\left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(6720 a^{3} b \,c^{4} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-8400 a^{2} b^{3} c^{3} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+2940 a \,b^{5} c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-315 b^{7} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+6720 \sqrt{c \,x^{2}+b x +a}\, a^{2} b \,c^{\frac{9}{2}} x -6720 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} c^{\frac{7}{2}} x +1260 \sqrt{c \,x^{2}+b x +a}\, b^{5} c^{\frac{5}{2}} x +3360 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} c^{\frac{7}{2}}-3360 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} c^{\frac{5}{2}}+4480 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b \,c^{\frac{9}{2}} x +630 \sqrt{c \,x^{2}+b x +a}\, b^{6} c^{\frac{3}{2}}-3360 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} c^{\frac{7}{2}} x +10240 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} c^{\frac{11}{2}} x^{2}+2240 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} c^{\frac{7}{2}}-1680 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} c^{\frac{5}{2}}-7680 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b \,c^{\frac{9}{2}} x -4096 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,c^{\frac{9}{2}}+5376 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{2} c^{\frac{7}{2}}\right)}{71680 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{\frac{13}{2}} x^{3}}"," ",0,"1/71680*(c*x^4+b*x^3+a*x^2)^(3/2)*(10240*x^2*(c*x^2+b*x+a)^(5/2)*c^(11/2)-7680*c^(9/2)*(c*x^2+b*x+a)^(5/2)*x*b-4096*c^(9/2)*(c*x^2+b*x+a)^(5/2)*a+5376*c^(7/2)*(c*x^2+b*x+a)^(5/2)*b^2+4480*c^(9/2)*(c*x^2+b*x+a)^(3/2)*x*a*b-3360*c^(7/2)*(c*x^2+b*x+a)^(3/2)*x*b^3+2240*c^(7/2)*(c*x^2+b*x+a)^(3/2)*a*b^2-1680*c^(5/2)*(c*x^2+b*x+a)^(3/2)*b^4+6720*c^(9/2)*(c*x^2+b*x+a)^(1/2)*x*a^2*b-6720*c^(7/2)*(c*x^2+b*x+a)^(1/2)*x*a*b^3+1260*c^(5/2)*(c*x^2+b*x+a)^(1/2)*x*b^5+3360*c^(7/2)*(c*x^2+b*x+a)^(1/2)*a^2*b^2-3360*c^(5/2)*(c*x^2+b*x+a)^(1/2)*a*b^4+630*c^(3/2)*(c*x^2+b*x+a)^(1/2)*b^6+6720*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a^3*b*c^4-8400*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a^2*b^3*c^3+2940*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a*b^5*c^2-315*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*b^7*c)/x^3/(c*x^2+b*x+a)^(3/2)/c^(13/2)","A"
40,1,431,258,0.009000," ","int((c*x^4+b*x^3+a*x^2)^(3/2)/x,x)","\frac{\left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(-960 a^{3} c^{4} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+2160 a^{2} b^{2} c^{3} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-900 a \,b^{4} c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+105 b^{6} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-960 \sqrt{c \,x^{2}+b x +a}\, a^{2} c^{\frac{9}{2}} x +1920 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} c^{\frac{7}{2}} x -420 \sqrt{c \,x^{2}+b x +a}\, b^{4} c^{\frac{5}{2}} x -480 \sqrt{c \,x^{2}+b x +a}\, a^{2} b \,c^{\frac{7}{2}}+960 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} c^{\frac{5}{2}}-640 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,c^{\frac{9}{2}} x -210 \sqrt{c \,x^{2}+b x +a}\, b^{5} c^{\frac{3}{2}}+1120 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} c^{\frac{7}{2}} x -320 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b \,c^{\frac{7}{2}}+560 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} c^{\frac{5}{2}}+2560 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} c^{\frac{9}{2}} x -1792 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b \,c^{\frac{7}{2}}\right)}{15360 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{\frac{11}{2}} x^{3}}"," ",0,"1/15360*(c*x^4+b*x^3+a*x^2)^(3/2)*(2560*x*(c*x^2+b*x+a)^(5/2)*c^(9/2)-1792*c^(7/2)*(c*x^2+b*x+a)^(5/2)*b-640*c^(9/2)*(c*x^2+b*x+a)^(3/2)*x*a+1120*c^(7/2)*(c*x^2+b*x+a)^(3/2)*x*b^2-320*c^(7/2)*(c*x^2+b*x+a)^(3/2)*a*b+560*c^(5/2)*(c*x^2+b*x+a)^(3/2)*b^3-960*c^(9/2)*(c*x^2+b*x+a)^(1/2)*x*a^2+1920*c^(7/2)*(c*x^2+b*x+a)^(1/2)*x*a*b^2-420*c^(5/2)*(c*x^2+b*x+a)^(1/2)*x*b^4-480*c^(7/2)*(c*x^2+b*x+a)^(1/2)*a^2*b+960*c^(5/2)*(c*x^2+b*x+a)^(1/2)*a*b^3-210*c^(3/2)*(c*x^2+b*x+a)^(1/2)*b^5-960*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a^3*c^4+2160*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a^2*b^2*c^3-900*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a*b^4*c^2+105*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*b^6*c)/x^3/(c*x^2+b*x+a)^(3/2)/c^(11/2)","A"
41,1,289,172,0.007000," ","int((c*x^4+b*x^3+a*x^2)^(3/2)/x^2,x)","\frac{\left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(-240 a^{2} b \,c^{3} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+120 a \,b^{3} c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-15 b^{5} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-240 \sqrt{c \,x^{2}+b x +a}\, a b \,c^{\frac{7}{2}} x +60 \sqrt{c \,x^{2}+b x +a}\, b^{3} c^{\frac{5}{2}} x -120 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} c^{\frac{5}{2}}+30 \sqrt{c \,x^{2}+b x +a}\, b^{4} c^{\frac{3}{2}}-160 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,c^{\frac{7}{2}} x -80 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} c^{\frac{5}{2}}+256 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} c^{\frac{7}{2}}\right)}{1280 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{\frac{9}{2}} x^{3}}"," ",0,"1/1280*(c*x^4+b*x^3+a*x^2)^(3/2)*(256*(c*x^2+b*x+a)^(5/2)*c^(7/2)-160*(c*x^2+b*x+a)^(3/2)*b*c^(7/2)*x-80*(c*x^2+b*x+a)^(3/2)*b^2*c^(5/2)-240*(c*x^2+b*x+a)^(1/2)*a*b*c^(7/2)*x+60*(c*x^2+b*x+a)^(1/2)*b^3*c^(5/2)*x-120*(c*x^2+b*x+a)^(1/2)*a*b^2*c^(5/2)+30*(c*x^2+b*x+a)^(1/2)*b^4*c^(3/2)-240*a^2*b*c^3*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))+120*a*b^3*c^2*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))-15*b^5*c*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2)))/x^3/(c*x^2+b*x+a)^(3/2)/c^(9/2)","A"
42,1,265,143,0.005000," ","int((c*x^4+b*x^3+a*x^2)^(3/2)/x^3,x)","\frac{\left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(48 a^{2} c^{3} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-24 a \,b^{2} c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+3 b^{4} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+48 \sqrt{c \,x^{2}+b x +a}\, a \,c^{\frac{7}{2}} x -12 \sqrt{c \,x^{2}+b x +a}\, b^{2} c^{\frac{5}{2}} x +24 \sqrt{c \,x^{2}+b x +a}\, a b \,c^{\frac{5}{2}}-6 \sqrt{c \,x^{2}+b x +a}\, b^{3} c^{\frac{3}{2}}+32 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{\frac{7}{2}} x +16 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,c^{\frac{5}{2}}\right)}{128 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{\frac{7}{2}} x^{3}}"," ",0,"1/128*(c*x^4+b*x^3+a*x^2)^(3/2)*(32*(c*x^2+b*x+a)^(3/2)*c^(7/2)*x+16*(c*x^2+b*x+a)^(3/2)*b*c^(5/2)+48*(c*x^2+b*x+a)^(1/2)*a*c^(7/2)*x-12*(c*x^2+b*x+a)^(1/2)*b^2*c^(5/2)*x+24*(c*x^2+b*x+a)^(1/2)*a*b*c^(5/2)-6*(c*x^2+b*x+a)^(1/2)*b^3*c^(3/2)+48*a^2*c^3*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))-24*a*b^2*c^2*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))+3*b^4*c*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2)))/x^3/(c*x^2+b*x+a)^(3/2)/c^(7/2)","A"
43,1,222,193,0.006000," ","int((c*x^4+b*x^3+a*x^2)^(3/2)/x^4,x)","-\frac{\left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(48 a^{\frac{3}{2}} c^{\frac{5}{2}} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-36 a b \,c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+3 b^{3} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-12 \sqrt{c \,x^{2}+b x +a}\, b \,c^{\frac{5}{2}} x -48 \sqrt{c \,x^{2}+b x +a}\, a \,c^{\frac{5}{2}}-6 \sqrt{c \,x^{2}+b x +a}\, b^{2} c^{\frac{3}{2}}-16 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{\frac{5}{2}}\right)}{48 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{\frac{5}{2}} x^{3}}"," ",0,"-1/48*(c*x^4+b*x^3+a*x^2)^(3/2)*(48*c^(5/2)*a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)-16*(c*x^2+b*x+a)^(3/2)*c^(5/2)-12*(c*x^2+b*x+a)^(1/2)*b*c^(5/2)*x-48*c^(5/2)*(c*x^2+b*x+a)^(1/2)*a-6*(c*x^2+b*x+a)^(1/2)*b^2*c^(3/2)-36*a*b*c^2*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))+3*b^3*c*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2)))/x^3/(c*x^2+b*x+a)^(3/2)/c^(5/2)","A"
44,1,254,185,0.006000," ","int((c*x^4+b*x^3+a*x^2)^(3/2)/x^5,x)","\frac{\left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(12 a^{2} c^{2} x \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-12 a^{\frac{3}{2}} b \,c^{\frac{3}{2}} x \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+3 a \,b^{2} c x \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+12 \sqrt{c \,x^{2}+b x +a}\, a \,c^{\frac{5}{2}} x^{2}+18 \sqrt{c \,x^{2}+b x +a}\, a b \,c^{\frac{3}{2}} x +8 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{\frac{5}{2}} x^{2}+8 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,c^{\frac{3}{2}} x -8 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} c^{\frac{3}{2}}\right)}{8 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,c^{\frac{3}{2}} x^{4}}"," ",0,"1/8*(c*x^4+b*x^3+a*x^2)^(3/2)*(8*c^(5/2)*(c*x^2+b*x+a)^(3/2)*x^2+12*c^(5/2)*(c*x^2+b*x+a)^(1/2)*x^2*a-12*c^(3/2)*a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x*b-8*(c*x^2+b*x+a)^(5/2)*c^(3/2)+8*c^(3/2)*(c*x^2+b*x+a)^(3/2)*x*b+18*c^(3/2)*(c*x^2+b*x+a)^(1/2)*x*a*b+12*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*x*a^2*c^2+3*c*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*x*a*b^2)/x^4/(c*x^2+b*x+a)^(3/2)/a/c^(3/2)","A"
45,1,338,183,0.007000," ","int((c*x^4+b*x^3+a*x^2)^(3/2)/x^6,x)","-\frac{\left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(12 a^{\frac{5}{2}} c^{\frac{5}{2}} x^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-12 a^{2} b \,c^{2} x^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+3 a^{\frac{3}{2}} b^{2} c^{\frac{3}{2}} x^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-6 \sqrt{c \,x^{2}+b x +a}\, a b \,c^{\frac{5}{2}} x^{3}-12 \sqrt{c \,x^{2}+b x +a}\, a^{2} c^{\frac{5}{2}} x^{2}-6 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} c^{\frac{3}{2}} x^{2}-2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,c^{\frac{5}{2}} x^{3}-4 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,c^{\frac{5}{2}} x^{2}-2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} c^{\frac{3}{2}} x^{2}+2 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b \,c^{\frac{3}{2}} x +4 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,c^{\frac{3}{2}}\right)}{8 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} c^{\frac{3}{2}} x^{5}}"," ",0,"-1/8*(c*x^4+b*x^3+a*x^2)^(3/2)*(12*c^(5/2)*a^(5/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^2-2*c^(5/2)*(c*x^2+b*x+a)^(3/2)*x^3*b-4*c^(5/2)*(c*x^2+b*x+a)^(3/2)*x^2*a-6*c^(5/2)*(c*x^2+b*x+a)^(1/2)*x^3*a*b+3*c^(3/2)*a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^2*b^2-12*c^(5/2)*(c*x^2+b*x+a)^(1/2)*x^2*a^2+2*c^(3/2)*(c*x^2+b*x+a)^(5/2)*x*b-2*c^(3/2)*(c*x^2+b*x+a)^(3/2)*x^2*b^2+4*(c*x^2+b*x+a)^(5/2)*a*c^(3/2)-6*c^(3/2)*(c*x^2+b*x+a)^(1/2)*x^2*a*b^2-12*c^2*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*x^2*a^2*b)/x^5/(c*x^2+b*x+a)^(3/2)/a^2/c^(3/2)","A"
46,1,435,219,0.009000," ","int((c*x^4+b*x^3+a*x^2)^(3/2)/x^7,x)","\frac{\left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(48 a^{3} c^{3} x^{3} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-36 a^{\frac{5}{2}} b \,c^{\frac{5}{2}} x^{3} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+3 a^{\frac{3}{2}} b^{3} c^{\frac{3}{2}} x^{3} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+48 \sqrt{c \,x^{2}+b x +a}\, a^{2} c^{\frac{7}{2}} x^{4}-6 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} c^{\frac{5}{2}} x^{4}+60 \sqrt{c \,x^{2}+b x +a}\, a^{2} b \,c^{\frac{5}{2}} x^{3}-6 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} c^{\frac{3}{2}} x^{3}+32 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,c^{\frac{7}{2}} x^{4}-2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} c^{\frac{5}{2}} x^{4}+28 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b \,c^{\frac{5}{2}} x^{3}-2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} c^{\frac{3}{2}} x^{3}-32 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,c^{\frac{5}{2}} x^{2}+2 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{2} c^{\frac{3}{2}} x^{2}+4 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a b \,c^{\frac{3}{2}} x -16 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a^{2} c^{\frac{3}{2}}\right)}{48 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{3} c^{\frac{3}{2}} x^{6}}"," ",0,"1/48*(c*x^4+b*x^3+a*x^2)^(3/2)*(32*c^(7/2)*(c*x^2+b*x+a)^(3/2)*x^4*a-36*c^(5/2)*a^(5/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^3*b+48*c^(7/2)*(c*x^2+b*x+a)^(1/2)*x^4*a^2-2*c^(5/2)*(c*x^2+b*x+a)^(3/2)*x^4*b^2-32*c^(5/2)*(c*x^2+b*x+a)^(5/2)*x^2*a+28*c^(5/2)*(c*x^2+b*x+a)^(3/2)*x^3*a*b-6*c^(5/2)*(c*x^2+b*x+a)^(1/2)*x^4*a*b^2+3*c^(3/2)*a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^3*b^3+60*c^(5/2)*(c*x^2+b*x+a)^(1/2)*x^3*a^2*b+2*c^(3/2)*(c*x^2+b*x+a)^(5/2)*x^2*b^2-2*c^(3/2)*(c*x^2+b*x+a)^(3/2)*x^3*b^3+4*c^(3/2)*(c*x^2+b*x+a)^(5/2)*x*a*b-6*c^(3/2)*(c*x^2+b*x+a)^(1/2)*x^3*a*b^3-16*(c*x^2+b*x+a)^(5/2)*a^2*c^(3/2)+48*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*x^3*a^3*c^3)/x^6/(c*x^2+b*x+a)^(3/2)/a^3/c^(3/2)","A"
47,1,501,171,0.007000," ","int((c*x^4+b*x^3+a*x^2)^(3/2)/x^8,x)","-\frac{\left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(48 a^{\frac{7}{2}} c^{2} x^{4} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-24 a^{\frac{5}{2}} b^{2} c \,x^{4} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+3 a^{\frac{3}{2}} b^{4} x^{4} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+24 \sqrt{c \,x^{2}+b x +a}\, a^{2} b \,c^{2} x^{5}-6 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} c \,x^{5}-48 \sqrt{c \,x^{2}+b x +a}\, a^{3} c^{2} x^{4}+36 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} c \,x^{4}-6 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} x^{4}+24 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b \,c^{2} x^{5}-2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} c \,x^{5}-16 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} c^{2} x^{4}+20 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} c \,x^{4}-2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} x^{4}-24 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a b c \,x^{3}+2 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{3} x^{3}+16 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a^{2} c \,x^{2}+4 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,b^{2} x^{2}-16 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a^{2} b x +32 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a^{3}\right)}{128 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{4} x^{7}}"," ",0,"-1/128*(c*x^4+b*x^3+a*x^2)^(3/2)*(48*c^2*a^(7/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^4+24*c^2*(c*x^2+b*x+a)^(3/2)*x^5*a*b-24*c*a^(5/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^4*b^2-16*c^2*(c*x^2+b*x+a)^(3/2)*x^4*a^2+24*c^2*(c*x^2+b*x+a)^(1/2)*x^5*a^2*b-2*c*(c*x^2+b*x+a)^(3/2)*x^5*b^3-48*c^2*(c*x^2+b*x+a)^(1/2)*x^4*a^3-24*c*(c*x^2+b*x+a)^(5/2)*x^3*a*b+20*c*(c*x^2+b*x+a)^(3/2)*x^4*a*b^2-6*c*(c*x^2+b*x+a)^(1/2)*x^5*a*b^3+3*a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^4*b^4+16*c*(c*x^2+b*x+a)^(5/2)*x^2*a^2+36*c*(c*x^2+b*x+a)^(1/2)*x^4*a^2*b^2+2*(c*x^2+b*x+a)^(5/2)*x^3*b^3-2*(c*x^2+b*x+a)^(3/2)*x^4*b^4+4*(c*x^2+b*x+a)^(5/2)*x^2*a*b^2-6*(c*x^2+b*x+a)^(1/2)*x^4*a*b^4-16*(c*x^2+b*x+a)^(5/2)*x*a^2*b+32*(c*x^2+b*x+a)^(5/2)*a^3)/x^7/(c*x^2+b*x+a)^(3/2)/a^4","B"
48,1,534,219,0.010000," ","int((c*x^4+b*x^3+a*x^2)^(3/2)/x^9,x)","\frac{\left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(240 a^{\frac{7}{2}} b \,c^{2} x^{5} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-120 a^{\frac{5}{2}} b^{3} c \,x^{5} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+15 a^{\frac{3}{2}} b^{5} x^{5} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+120 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} c^{2} x^{6}-30 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} c \,x^{6}-240 \sqrt{c \,x^{2}+b x +a}\, a^{3} b \,c^{2} x^{5}+180 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{3} c \,x^{5}-30 \sqrt{c \,x^{2}+b x +a}\, a \,b^{5} x^{5}+120 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} c^{2} x^{6}-10 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} c \,x^{6}-80 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} b \,c^{2} x^{5}+100 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{3} c \,x^{5}-10 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{5} x^{5}-120 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,b^{2} c \,x^{4}+10 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{4} x^{4}+80 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a^{2} b c \,x^{3}+20 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,b^{3} x^{3}-80 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a^{2} b^{2} x^{2}+160 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a^{3} b x -256 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a^{4}\right)}{1280 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{5} x^{8}}"," ",0,"1/1280*(c*x^4+b*x^3+a*x^2)^(3/2)*(240*c^2*a^(7/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^5*b+120*c^2*(c*x^2+b*x+a)^(3/2)*x^6*a*b^2-120*c*a^(5/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^5*b^3-80*c^2*(c*x^2+b*x+a)^(3/2)*x^5*a^2*b+120*c^2*(c*x^2+b*x+a)^(1/2)*x^6*a^2*b^2-10*c*(c*x^2+b*x+a)^(3/2)*x^6*b^4-240*c^2*(c*x^2+b*x+a)^(1/2)*x^5*a^3*b-120*c*(c*x^2+b*x+a)^(5/2)*x^4*a*b^2+100*c*(c*x^2+b*x+a)^(3/2)*x^5*a*b^3-30*c*(c*x^2+b*x+a)^(1/2)*x^6*a*b^4+15*a^(3/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^5*b^5+80*c*(c*x^2+b*x+a)^(5/2)*x^3*a^2*b+180*c*(c*x^2+b*x+a)^(1/2)*x^5*a^2*b^3+10*(c*x^2+b*x+a)^(5/2)*x^4*b^4-10*(c*x^2+b*x+a)^(3/2)*x^5*b^5+20*(c*x^2+b*x+a)^(5/2)*x^3*a*b^3-30*(c*x^2+b*x+a)^(1/2)*x^5*a*b^5-80*(c*x^2+b*x+a)^(5/2)*x^2*a^2*b^2+160*(c*x^2+b*x+a)^(5/2)*x*a^3*b-256*(c*x^2+b*x+a)^(5/2)*a^4)/x^8/(c*x^2+b*x+a)^(3/2)/a^5","B"
49,1,144,121,0.009000," ","int(x^3/(c*x^4+b*x^3+a*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \left(-4 a \,c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+3 b^{2} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+4 \sqrt{c \,x^{2}+b x +a}\, c^{\frac{5}{2}} x -6 \sqrt{c \,x^{2}+b x +a}\, b \,c^{\frac{3}{2}}\right) x}{8 \sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, c^{\frac{7}{2}}}"," ",0,"1/8*x*(c*x^2+b*x+a)^(1/2)*(4*(c*x^2+b*x+a)^(1/2)*c^(5/2)*x-6*(c*x^2+b*x+a)^(1/2)*b*c^(3/2)-4*a*c^2*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))+3*b^2*c*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2)))/(c*x^4+b*x^3+a*x^2)^(1/2)/c^(7/2)","A"
50,1,88,87,0.006000," ","int(x^2/(c*x^4+b*x^3+a*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, \left(-b c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+2 \sqrt{c \,x^{2}+b x +a}\, c^{\frac{3}{2}}\right) x}{2 \sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, c^{\frac{5}{2}}}"," ",0,"1/2*x*(c*x^2+b*x+a)^(1/2)*(2*(c*x^2+b*x+a)^(1/2)*c^(3/2)-b*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*c)/(c*x^4+b*x^3+a*x^2)^(1/2)/c^(5/2)","A"
51,1,65,59,0.006000," ","int(x/(c*x^4+b*x^3+a*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, x \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)}{\sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, \sqrt{c}}"," ",0,"1/(c*x^4+b*x^3+a*x^2)^(1/2)*x*(c*x^2+b*x+a)^(1/2)*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))/c^(1/2)","A"
52,1,66,37,0.005000," ","int(1/(c*x^4+b*x^3+a*x^2)^(1/2),x)","-\frac{\sqrt{c \,x^{2}+b x +a}\, x \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, \sqrt{a}}"," ",0,"-1/(c*x^4+b*x^3+a*x^2)^(1/2)*x*(c*x^2+b*x+a)^(1/2)/a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)","A"
53,1,88,65,0.007000," ","int(1/x/(c*x^4+b*x^3+a*x^2)^(1/2),x)","-\frac{\sqrt{c \,x^{2}+b x +a}\, \left(-a b x \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+2 \sqrt{c \,x^{2}+b x +a}\, a^{\frac{3}{2}}\right)}{2 \sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, a^{\frac{5}{2}}}"," ",0,"-1/2*(c*x^2+b*x+a)^(1/2)*(2*(c*x^2+b*x+a)^(1/2)*a^(3/2)-b*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*a*x)/(c*x^4+b*x^3+a*x^2)^(1/2)/a^(5/2)","A"
54,1,152,101,0.007000," ","int(1/x^2/(c*x^4+b*x^3+a*x^2)^(1/2),x)","-\frac{\sqrt{c \,x^{2}+b x +a}\, \left(-4 a^{2} c \,x^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+3 a \,b^{2} x^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-6 \sqrt{c \,x^{2}+b x +a}\, a^{\frac{3}{2}} b x +4 \sqrt{c \,x^{2}+b x +a}\, a^{\frac{5}{2}}\right)}{8 \sqrt{c \,x^{4}+b \,x^{3}+a \,x^{2}}\, a^{\frac{7}{2}} x}"," ",0,"-1/8*(c*x^2+b*x+a)^(1/2)*(4*(c*x^2+b*x+a)^(1/2)*a^(5/2)-6*(c*x^2+b*x+a)^(1/2)*a^(3/2)*x*b-4*c*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^2*a^2+3*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^2*a*b^2)/x/(c*x^4+b*x^3+a*x^2)^(1/2)/a^(7/2)","A"
55,1,283,236,0.009000," ","int(x^7/(c*x^4+b*x^3+a*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b x +a \right) \left(16 a \,c^{\frac{9}{2}} x^{3}-4 b^{2} c^{\frac{7}{2}} x^{3}-40 a b \,c^{\frac{7}{2}} x^{2}+10 b^{3} c^{\frac{5}{2}} x^{2}+48 a^{2} c^{\frac{7}{2}} x -124 a \,b^{2} c^{\frac{5}{2}} x +30 b^{4} c^{\frac{3}{2}} x -48 \sqrt{c \,x^{2}+b x +a}\, a^{2} c^{3} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+72 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-15 \sqrt{c \,x^{2}+b x +a}\, b^{4} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-104 a^{2} b \,c^{\frac{5}{2}}+30 a \,b^{3} c^{\frac{3}{2}}\right) x^{3}}{8 \left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(4 a c -b^{2}\right) c^{\frac{9}{2}}}"," ",0,"1/8*x^3*(c*x^2+b*x+a)/c^(9/2)*(16*c^(9/2)*x^3*a-4*c^(7/2)*x^3*b^2-40*c^(7/2)*x^2*a*b+10*c^(5/2)*x^2*b^3+48*c^(7/2)*x*a^2-124*c^(5/2)*x*a*b^2+30*c^(3/2)*x*b^4-104*c^(5/2)*a^2*b+30*c^(3/2)*a*b^3-48*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*(c*x^2+b*x+a)^(1/2)*a^2*c^3+72*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*(c*x^2+b*x+a)^(1/2)*a*b^2*c^2-15*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*(c*x^2+b*x+a)^(1/2)*b^4*c)/(c*x^4+b*x^3+a*x^2)^(3/2)/(4*a*c-b^2)","A"
56,1,199,181,0.009000," ","int(x^6/(c*x^4+b*x^3+a*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b x +a \right) \left(8 a \,c^{\frac{7}{2}} x^{2}-2 b^{2} c^{\frac{5}{2}} x^{2}+20 a b \,c^{\frac{5}{2}} x -6 b^{3} c^{\frac{3}{2}} x -12 \sqrt{c \,x^{2}+b x +a}\, a b \,c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+3 \sqrt{c \,x^{2}+b x +a}\, b^{3} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+16 a^{2} c^{\frac{5}{2}}-6 a \,b^{2} c^{\frac{3}{2}}\right) x^{3}}{2 \left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(4 a c -b^{2}\right) c^{\frac{7}{2}}}"," ",0,"1/2*x^3*(c*x^2+b*x+a)/c^(7/2)*(8*c^(7/2)*x^2*a-2*c^(5/2)*x^2*b^2+20*c^(5/2)*x*a*b-6*c^(3/2)*x*b^3+16*c^(5/2)*a^2-6*c^(3/2)*a*b^2-12*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*(c*x^2+b*x+a)^(1/2)*a*b*c^2+3*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*(c*x^2+b*x+a)^(1/2)*b^3*c)/(c*x^4+b*x^3+a*x^2)^(3/2)/(4*a*c-b^2)","A"
57,1,166,137,0.007000," ","int(x^5/(c*x^4+b*x^3+a*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b x +a \right) \left(-4 a \,c^{\frac{5}{2}} x +2 b^{2} c^{\frac{3}{2}} x +4 \sqrt{c \,x^{2}+b x +a}\, a \,c^{2} \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)-\sqrt{c \,x^{2}+b x +a}\, b^{2} c \ln \left(\frac{2 c x +b +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{c}}{2 \sqrt{c}}\right)+2 a b \,c^{\frac{3}{2}}\right) x^{3}}{\left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(4 a c -b^{2}\right) c^{\frac{5}{2}}}"," ",0,"x^3*(c*x^2+b*x+a)/c^(5/2)*(-4*c^(5/2)*x*a+2*c^(3/2)*x*b^2+4*(c*x^2+b*x+a)^(1/2)*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*a*c^2-(c*x^2+b*x+a)^(1/2)*ln(1/2*(2*c*x+b+2*(c*x^2+b*x+a)^(1/2)*c^(1/2))/c^(1/2))*b^2*c+2*c^(3/2)*a*b)/(c*x^4+b*x^3+a*x^2)^(3/2)/(4*a*c-b^2)","A"
58,1,53,38,0.004000," ","int(x^4/(c*x^4+b*x^3+a*x^2)^(3/2),x)","-\frac{2 \left(c \,x^{2}+b x +a \right) \left(b x +2 a \right) x^{3}}{\left(4 a c -b^{2}\right) \left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}}}"," ",0,"-2*(c*x^2+b*x+a)*(b*x+2*a)*x^3/(4*a*c-b^2)/(c*x^4+b*x^3+a*x^2)^(3/2)","A"
59,1,52,37,0.003000," ","int(x^3/(c*x^4+b*x^3+a*x^2)^(3/2),x)","\frac{2 \left(c \,x^{2}+b x +a \right) \left(2 c x +b \right) x^{3}}{\left(4 a c -b^{2}\right) \left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}}}"," ",0,"2*(c*x^2+b*x+a)*(2*c*x+b)*x^3/(4*a*c-b^2)/(c*x^4+b*x^3+a*x^2)^(3/2)","A"
60,1,166,84,0.008000," ","int(x^2/(c*x^4+b*x^3+a*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b x +a \right) \left(2 a^{\frac{3}{2}} b c x +4 \sqrt{c \,x^{2}+b x +a}\, a^{2} c \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-\sqrt{c \,x^{2}+b x +a}\, a \,b^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-4 a^{\frac{5}{2}} c +2 a^{\frac{3}{2}} b^{2}\right) x^{3}}{\left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(4 a c -b^{2}\right) a^{\frac{5}{2}}}"," ",0,"-x^3*(c*x^2+b*x+a)*(2*a^(3/2)*x*b*c+4*(c*x^2+b*x+a)^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*a^2*c-(c*x^2+b*x+a)^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*a*b^2-4*a^(5/2)*c+2*a^(3/2)*b^2)/(c*x^4+b*x^3+a*x^2)^(3/2)/a^(5/2)/(4*a*c-b^2)","A"
61,1,201,130,0.009000," ","int(x/(c*x^4+b*x^3+a*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b x +a \right) \left(-16 a^{\frac{5}{2}} c^{2} x^{2}+6 a^{\frac{3}{2}} b^{2} c \,x^{2}+12 \sqrt{c \,x^{2}+b x +a}\, a^{2} b c x \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} x \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-20 a^{\frac{5}{2}} b c x +6 a^{\frac{3}{2}} b^{3} x -8 a^{\frac{7}{2}} c +2 a^{\frac{5}{2}} b^{2}\right) x^{2}}{2 \left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(4 a c -b^{2}\right) a^{\frac{7}{2}}}"," ",0,"1/2*x^2*(c*x^2+b*x+a)*(-16*a^(5/2)*x^2*c^2+6*a^(3/2)*x^2*b^2*c+12*(c*x^2+b*x+a)^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x*a^2*b*c-3*(c*x^2+b*x+a)^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x*a*b^3-20*a^(5/2)*x*b*c+6*a^(3/2)*x*b^3-8*a^(7/2)*c+2*a^(5/2)*b^2)/(c*x^4+b*x^3+a*x^2)^(3/2)/a^(7/2)/(4*a*c-b^2)","A"
62,1,292,189,0.009000," ","int(1/(c*x^4+b*x^3+a*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b x +a \right) \left(-104 a^{\frac{5}{2}} b \,c^{2} x^{3}+30 a^{\frac{3}{2}} b^{3} c \,x^{3}-48 \sqrt{c \,x^{2}+b x +a}\, a^{3} c^{2} x^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+72 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} c \,x^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-15 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} x^{2} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+48 a^{\frac{7}{2}} c^{2} x^{2}-124 a^{\frac{5}{2}} b^{2} c \,x^{2}+30 a^{\frac{3}{2}} b^{4} x^{2}-40 a^{\frac{7}{2}} b c x +10 a^{\frac{5}{2}} b^{3} x +16 a^{\frac{9}{2}} c -4 a^{\frac{7}{2}} b^{2}\right) x}{8 \left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(4 a c -b^{2}\right) a^{\frac{9}{2}}}"," ",0,"-1/8*x*(c*x^2+b*x+a)*(48*a^(7/2)*x^2*c^2-104*a^(5/2)*x^3*b*c^2+16*a^(9/2)*c-40*a^(7/2)*x*b*c-124*a^(5/2)*x^2*b^2*c+30*a^(3/2)*x^3*b^3*c-4*a^(7/2)*b^2+10*a^(5/2)*x*b^3+30*a^(3/2)*x^2*b^4-48*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*(c*x^2+b*x+a)^(1/2)*x^2*a^3*c^2+72*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*(c*x^2+b*x+a)^(1/2)*x^2*a^2*b^2*c-15*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*(c*x^2+b*x+a)^(1/2)*x^2*a*b^4)/(c*x^4+b*x^3+a*x^2)^(3/2)/a^(9/2)/(4*a*c-b^2)","A"
63,1,340,247,0.010000," ","int(1/x/(c*x^4+b*x^3+a*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b x +a \right) \left(-512 a^{\frac{7}{2}} c^{3} x^{4}+920 a^{\frac{5}{2}} b^{2} c^{2} x^{4}-210 a^{\frac{3}{2}} b^{4} c \,x^{4}+720 \sqrt{c \,x^{2}+b x +a}\, a^{3} b \,c^{2} x^{3} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-600 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{3} c \,x^{3} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+105 \sqrt{c \,x^{2}+b x +a}\, a \,b^{5} x^{3} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-976 a^{\frac{7}{2}} b \,c^{2} x^{3}+1060 a^{\frac{5}{2}} b^{3} c \,x^{3}-210 a^{\frac{3}{2}} b^{5} x^{3}-256 a^{\frac{9}{2}} c^{2} x^{2}+344 a^{\frac{7}{2}} b^{2} c \,x^{2}-70 a^{\frac{5}{2}} b^{4} x^{2}-112 a^{\frac{9}{2}} b c x +28 a^{\frac{7}{2}} b^{3} x +64 a^{\frac{11}{2}} c -16 a^{\frac{9}{2}} b^{2}\right)}{48 \left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(4 a c -b^{2}\right) a^{\frac{11}{2}}}"," ",0,"-1/48*(c*x^2+b*x+a)*(-512*a^(7/2)*x^4*c^3-256*a^(9/2)*x^2*c^2-976*a^(7/2)*x^3*b*c^2+920*a^(5/2)*x^4*b^2*c^2+64*a^(11/2)*c-112*a^(9/2)*x*b*c+344*a^(7/2)*x^2*b^2*c+1060*a^(5/2)*x^3*b^3*c-210*a^(3/2)*x^4*b^4*c-16*a^(9/2)*b^2+28*a^(7/2)*x*b^3-70*a^(5/2)*x^2*b^4-210*a^(3/2)*x^3*b^5+720*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*(c*x^2+b*x+a)^(1/2)*x^3*a^3*b*c^2-600*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*(c*x^2+b*x+a)^(1/2)*x^3*a^2*b^3*c+105*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*(c*x^2+b*x+a)^(1/2)*x^3*a*b^5)/(c*x^4+b*x^3+a*x^2)^(3/2)/a^(11/2)/(4*a*c-b^2)","A"
64,1,446,315,0.011000," ","int(1/x^2/(c*x^4+b*x^3+a*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b x +a \right) \left(3616 a^{\frac{7}{2}} b \,c^{3} x^{5}-3360 a^{\frac{5}{2}} b^{3} c^{2} x^{5}+630 a^{\frac{3}{2}} b^{5} c \,x^{5}+960 \sqrt{c \,x^{2}+b x +a}\, a^{4} c^{3} x^{4} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-3600 \sqrt{c \,x^{2}+b x +a}\, a^{3} b^{2} c^{2} x^{4} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)+2100 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{4} c \,x^{4} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-315 \sqrt{c \,x^{2}+b x +a}\, a \,b^{6} x^{4} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)-960 a^{\frac{9}{2}} c^{3} x^{4}+5408 a^{\frac{7}{2}} b^{2} c^{2} x^{4}-3780 a^{\frac{5}{2}} b^{4} c \,x^{4}+630 a^{\frac{3}{2}} b^{6} x^{4}+1568 a^{\frac{9}{2}} b \,c^{2} x^{3}-1232 a^{\frac{7}{2}} b^{3} c \,x^{3}+210 a^{\frac{5}{2}} b^{5} x^{3}-320 a^{\frac{11}{2}} c^{2} x^{2}+416 a^{\frac{9}{2}} b^{2} c \,x^{2}-84 a^{\frac{7}{2}} b^{4} x^{2}-192 a^{\frac{11}{2}} b c x +48 a^{\frac{9}{2}} b^{3} x +128 a^{\frac{13}{2}} c -32 a^{\frac{11}{2}} b^{2}\right)}{128 \left(c \,x^{4}+b \,x^{3}+a \,x^{2}\right)^{\frac{3}{2}} \left(4 a c -b^{2}\right) a^{\frac{13}{2}} x}"," ",0,"-1/128/x*(c*x^2+b*x+a)*(3616*a^(7/2)*x^5*b*c^3-3360*a^(5/2)*x^5*b^3*c^2+630*a^(3/2)*x^5*b^5*c+960*(c*x^2+b*x+a)^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^4*a^4*c^3-3600*(c*x^2+b*x+a)^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^4*a^3*b^2*c^2+2100*(c*x^2+b*x+a)^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^4*a^2*b^4*c-315*(c*x^2+b*x+a)^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)*x^4*a*b^6-960*a^(9/2)*x^4*c^3+5408*a^(7/2)*x^4*b^2*c^2-3780*a^(5/2)*x^4*b^4*c+630*a^(3/2)*x^4*b^6+1568*a^(9/2)*x^3*b*c^2-1232*a^(7/2)*x^3*b^3*c+210*a^(5/2)*x^3*b^5-320*a^(11/2)*x^2*c^2+416*a^(9/2)*x^2*b^2*c-84*a^(7/2)*x^2*b^4-192*a^(11/2)*x*b*c+48*a^(9/2)*x*b^3+128*a^(13/2)*c-32*a^(11/2)*b^2)/(c*x^4+b*x^3+a*x^2)^(3/2)/a^(13/2)/(4*a*c-b^2)","A"
65,1,77,37,0.003000," ","int(x^m*(c*x^5+b*x^3+a*x),x)","\frac{\left(c \,m^{2} x^{4}+6 c m \,x^{4}+b \,m^{2} x^{2}+8 c \,x^{4}+8 b m \,x^{2}+a \,m^{2}+12 b \,x^{2}+10 a m +24 a \right) x^{m +2}}{\left(m +6\right) \left(m +4\right) \left(m +2\right)}"," ",0,"x^(m+2)*(c*m^2*x^4+6*c*m*x^4+b*m^2*x^2+8*c*x^4+8*b*m*x^2+a*m^2+12*b*x^2+10*a*m+24*a)/(m+6)/(m+4)/(m+2)","B"
66,1,20,19,0.002000," ","int(x^2*(c*x^5+b*x^3+a*x),x)","\frac{1}{8} c \,x^{8}+\frac{1}{6} b \,x^{6}+\frac{1}{4} a \,x^{4}"," ",0,"1/4*a*x^4+1/6*b*x^6+1/8*c*x^8","A"
67,1,20,19,0.002000," ","int(x*(c*x^5+b*x^3+a*x),x)","\frac{1}{7} c \,x^{7}+\frac{1}{5} b \,x^{5}+\frac{1}{3} a \,x^{3}"," ",0,"1/3*a*x^3+1/5*b*x^5+1/7*c*x^7","A"
68,1,20,19,0.002000," ","int(c*x^5+b*x^3+a*x,x)","\frac{1}{6} c \,x^{6}+\frac{1}{4} b \,x^{4}+\frac{1}{2} a \,x^{2}"," ",0,"1/2*a*x^2+1/4*b*x^4+1/6*c*x^6","A"
69,1,17,16,0.000000," ","int((c*x^5+b*x^3+a*x)/x,x)","\frac{1}{5} c \,x^{5}+\frac{1}{3} b \,x^{3}+a x"," ",0,"a*x+1/3*b*x^3+1/5*c*x^5","A"
70,1,18,17,0.001000," ","int((c*x^5+b*x^3+a*x)/x^2,x)","\frac{c \,x^{4}}{4}+\frac{b \,x^{2}}{2}+a \ln \left(x \right)"," ",0,"1/2*b*x^2+1/4*c*x^4+a*ln(x)","A"
71,1,17,16,0.003000," ","int((c*x^5+b*x^3+a*x)/x^3,x)","\frac{c \,x^{3}}{3}+b x -\frac{a}{x}"," ",0,"-a/x+b*x+1/3*c*x^3","A"
72,1,300,76,0.005000," ","int(x^m*(c*x^5+b*x^3+a*x)^2,x)","\frac{\left(c^{2} m^{4} x^{8}+24 c^{2} m^{3} x^{8}+2 b c \,m^{4} x^{6}+206 c^{2} m^{2} x^{8}+52 b c \,m^{3} x^{6}+744 c^{2} m \,x^{8}+2 a c \,m^{4} x^{4}+b^{2} m^{4} x^{4}+472 b c \,m^{2} x^{6}+945 c^{2} x^{8}+56 a c \,m^{3} x^{4}+28 b^{2} m^{3} x^{4}+1772 b c m \,x^{6}+2 a b \,m^{4} x^{2}+548 a c \,m^{2} x^{4}+274 b^{2} m^{2} x^{4}+2310 b c \,x^{6}+60 a b \,m^{3} x^{2}+2184 a c m \,x^{4}+1092 b^{2} m \,x^{4}+a^{2} m^{4}+640 a b \,m^{2} x^{2}+2970 a c \,x^{4}+1485 b^{2} x^{4}+32 a^{2} m^{3}+2820 a b m \,x^{2}+374 a^{2} m^{2}+4158 a b \,x^{2}+1888 a^{2} m +3465 a^{2}\right) x^{m +3}}{\left(m +11\right) \left(m +9\right) \left(m +7\right) \left(m +5\right) \left(m +3\right)}"," ",0,"x^(m+3)*(c^2*m^4*x^8+24*c^2*m^3*x^8+2*b*c*m^4*x^6+206*c^2*m^2*x^8+52*b*c*m^3*x^6+744*c^2*m*x^8+2*a*c*m^4*x^4+b^2*m^4*x^4+472*b*c*m^2*x^6+945*c^2*x^8+56*a*c*m^3*x^4+28*b^2*m^3*x^4+1772*b*c*m*x^6+2*a*b*m^4*x^2+548*a*c*m^2*x^4+274*b^2*m^2*x^4+2310*b*c*x^6+60*a*b*m^3*x^2+2184*a*c*m*x^4+1092*b^2*m*x^4+a^2*m^4+640*a*b*m^2*x^2+2970*a*c*x^4+1485*b^2*x^4+32*a^2*m^3+2820*a*b*m*x^2+374*a^2*m^2+4158*a*b*x^2+1888*a^2*m+3465*a^2)/(m+11)/(m+9)/(m+7)/(m+5)/(m+3)","B"
73,1,45,44,0.002000," ","int(x^2*(c*x^5+b*x^3+a*x)^2,x)","\frac{c^{2} x^{13}}{13}+\frac{2 b c \,x^{11}}{11}+\frac{2 a b \,x^{7}}{7}+\frac{\left(2 a c +b^{2}\right) x^{9}}{9}+\frac{a^{2} x^{5}}{5}"," ",0,"1/5*a^2*x^5+2/7*a*b*x^7+1/9*(2*a*c+b^2)*x^9+2/11*b*c*x^11+1/13*c^2*x^13","A"
74,1,45,44,0.000000," ","int(x*(c*x^5+b*x^3+a*x)^2,x)","\frac{c^{2} x^{12}}{12}+\frac{b c \,x^{10}}{5}+\frac{a b \,x^{6}}{3}+\frac{\left(2 a c +b^{2}\right) x^{8}}{8}+\frac{a^{2} x^{4}}{4}"," ",0,"1/4*a^2*x^4+1/3*a*b*x^6+1/8*(2*a*c+b^2)*x^8+1/5*b*c*x^10+1/12*c^2*x^12","A"
75,1,45,44,0.001000," ","int((c*x^5+b*x^3+a*x)^2,x)","\frac{c^{2} x^{11}}{11}+\frac{2 b c \,x^{9}}{9}+\frac{2 a b \,x^{5}}{5}+\frac{\left(2 a c +b^{2}\right) x^{7}}{7}+\frac{a^{2} x^{3}}{3}"," ",0,"1/3*a^2*x^3+2/5*a*b*x^5+1/7*(2*a*c+b^2)*x^7+2/9*b*c*x^9+1/11*c^2*x^11","A"
76,1,45,44,0.001000," ","int((c*x^5+b*x^3+a*x)^2/x,x)","\frac{c^{2} x^{10}}{10}+\frac{b c \,x^{8}}{4}+\frac{a b \,x^{4}}{2}+\frac{\left(2 a c +b^{2}\right) x^{6}}{6}+\frac{a^{2} x^{2}}{2}"," ",0,"1/2*a^2*x^2+1/2*a*b*x^4+1/6*(2*a*c+b^2)*x^6+1/4*b*c*x^8+1/10*c^2*x^10","A"
77,1,42,41,0.001000," ","int((c*x^5+b*x^3+a*x)^2/x^2,x)","\frac{c^{2} x^{9}}{9}+\frac{2 b c \,x^{7}}{7}+\frac{2 a b \,x^{3}}{3}+\frac{\left(2 a c +b^{2}\right) x^{5}}{5}+a^{2} x"," ",0,"a^2*x+2/3*a*b*x^3+1/5*(2*a*c+b^2)*x^5+2/7*b*c*x^7+1/9*c^2*x^9","A"
78,1,142,88,0.004000," ","int(x^8/(c*x^5+b*x^3+a*x),x)","\frac{x^{4}}{4 c}+\frac{3 a b \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^{3} \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 \,x^{2}}{2 c^{2}}-\frac{a \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}+\frac{b^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{3}}"," ",0,"1/4/c*x^4-1/2*b/c^2*x^2-1/4/c^2*ln(c*x^4+b*x^2+a)*a+1/4/c^3*ln(c*x^4+b*x^2+a)*b^2+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-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","A"
79,1,467,167,0.025000," ","int(x^7/(c*x^5+b*x^3+a*x),x)","-\frac{3 \sqrt{2}\, a b \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 \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^{3} \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} \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{x^{3}}{3 c}+\frac{\sqrt{2}\, a \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 \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} \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} \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{b x}{c^{2}}"," ",0,"1/3/c*x^3-b/c^2*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-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^2-3/2/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+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^3-1/2/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+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^2-3/2/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+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","B"
80,1,111,71,0.004000," ","int(x^6/(c*x^5+b*x^3+a*x),x)","-\frac{a \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} \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{x^{2}}{2 c}-\frac{b \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}"," ",0,"1/2/c*x^2-1/4*b*ln(c*x^4+b*x^2+a)/c^2-1/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a+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","A"
81,1,343,144,0.014000," ","int(x^5/(c*x^5+b*x^3+a*x),x)","\frac{\sqrt{2}\, a \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 \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} \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} \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 \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 \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{x}{c}"," ",0,"1/c*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)*b+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-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^2-1/2/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+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-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","B"
82,1,60,55,0.003000," ","int(x^4/(c*x^5+b*x^3+a*x),x)","-\frac{b \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c}+\frac{\ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c}"," ",0,"1/4*ln(c*x^4+b*x^2+a)/c-1/2*b/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","A"
83,1,208,115,0.011000," ","int(x^3/(c*x^5+b*x^3+a*x),x)","\frac{\sqrt{2}\, b \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 \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}\, \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}\, \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}}"," ",0,"-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)+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+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)+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","A"
84,1,36,32,0.003000," ","int(x^2/(c*x^5+b*x^3+a*x),x)","\frac{\arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}"," ",0,"1/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","A"
85,1,116,114,0.013000," ","int(x/(c*x^5+b*x^3+a*x),x)","-\frac{\sqrt{2}\, c \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 \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}}"," ",0,"-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)-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"
86,1,66,61,0.007000," ","int(1/(c*x^5+b*x^3+a*x),x)","-\frac{b \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a}+\frac{\ln \left(x \right)}{a}-\frac{\ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a}"," ",0,"1/a*ln(x)-1/4*ln(c*x^4+b*x^2+a)/a-1/2/a*b/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","A"
87,1,232,138,0.018000," ","int(1/x/(c*x^5+b*x^3+a*x),x)","\frac{\sqrt{2}\, b c \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 \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 \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 \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{1}{a x}"," ",0,"-1/a/x+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)+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-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)+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","A"
88,1,119,79,0.007000," ","int(1/x^2/(c*x^5+b*x^3+a*x),x)","-\frac{c \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} \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 \ln \left(x \right)}{a^{2}}+\frac{b \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a^{2}}-\frac{1}{2 a \,x^{2}}"," ",0,"-1/2/a/x^2-1/a^2*b*ln(x)+1/4*b*ln(c*x^4+b*x^2+a)/a^2-1/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c+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","A"
89,1,383,156,0.013000," ","int(x^11/(c*x^5+b*x^3+a*x)^2,x)","\frac{a^{2} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{2 a \,b^{2} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{b^{4} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{6 a^{2} \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} \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{b^{4} \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{3 a^{2} b}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{a \,b^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{2 a b \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) c^{2}}+\frac{b^{3} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(4 a c -b^{2}\right) c^{3}}+\frac{x^{2}}{2 c^{2}}"," ",0,"1/2*x^2/c^2+1/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a^2-2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a*b^2+1/2/c^3/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*b^4-3/2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a^2*b+1/2/c^3/(c*x^4+b*x^2+a)/(4*a*c-b^2)*a*b^3-2/c^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*a*b+1/2/c^3/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^3-6/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^2+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^2-1/c^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^4","B"
90,1,844,284,0.036000," ","int(x^10/(c*x^5+b*x^3+a*x)^2,x)","\frac{3 a b \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{b^{3} x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{5 \sqrt{2}\, 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{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{5 \sqrt{2}\, 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{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{19 \sqrt{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) \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} \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 \sqrt{2}\, 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) \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} \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{a^{2} x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{a \,b^{2} x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{13 \sqrt{2}\, a 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{13 \sqrt{2}\, a 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{3 \sqrt{2}\, 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^{2}}+\frac{3 \sqrt{2}\, 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^{2}}+\frac{x}{c^{2}}"," ",0,"1/c^2*x+3/2/c/(c*x^4+b*x^2+a)*b/(4*a*c-b^2)*x^3*a-1/2/c^2/(c*x^4+b*x^2+a)*b^3/(4*a*c-b^2)*x^3+1/c/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*x-1/2/c^2/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*b^2+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-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+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^2-19/4/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+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^4-13/4/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+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+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^2-19/4/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+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","B"
91,1,222,120,0.012000," ","int(x^9/(c*x^5+b*x^3+a*x)^2,x)","-\frac{3 a b \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{b^{3} \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{a \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) c}-\frac{b^{2} \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 c -b^{2}\right) b \,x^{2}}{\left(4 a c -b^{2}\right) c^{2}}+\frac{\left(2 a c -b^{2}\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*c-b^2)/(4*a*c-b^2)*b/c^2*x^2+(2*a*c-b^2)/(4*a*c-b^2)*a/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-1/4/c^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^2-3/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b+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","A"
92,1,602,227,0.029000," ","int(x^8/(c*x^5+b*x^3+a*x)^2,x)","\frac{2 \sqrt{2}\, 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{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, 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{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, 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{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, 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{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, a \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 \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} \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} \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{\frac{a b x}{2 \left(4 a c -b^{2}\right) c}-\frac{\left(2 a c -b^{2}\right) x^{3}}{2 \left(4 a c -b^{2}\right) c}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2*(2*a*c-b^2)/(4*a*c-b^2)/c*x^3+1/2/(4*a*c-b^2)*a*b/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+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+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-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+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-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+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-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","B"
93,1,104,72,0.010000," ","int(x^7/(c*x^5+b*x^3+a*x)^2,x)","\frac{2 a \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{a b}{\left(4 a c -b^{2}\right) c}-\frac{\left(2 a c -b^{2}\right) x^{2}}{\left(4 a c -b^{2}\right) c}}{2 c \,x^{4}+2 b \,x^{2}+2 a}"," ",0,"1/2*(-(2*a*c-b^2)/(4*a*c-b^2)/c*x^2+1/(4*a*c-b^2)*a*b/c)/(c*x^4+b*x^2+a)+2*a/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","A"
94,1,452,194,0.026000," ","int(x^6/(c*x^5+b*x^3+a*x)^2,x)","-\frac{\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{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\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{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, 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) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, 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) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, 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}}-\frac{\sqrt{2}\, 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}}+\frac{-\frac{b \,x^{3}}{2 \left(4 a c -b^{2}\right)}-\frac{a x}{4 a c -b^{2}}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2/(4*a*c-b^2)*b*x^3-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-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-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^2-1/4/(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-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-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","B"
95,1,77,69,0.006000," ","int(x^5/(c*x^5+b*x^3+a*x)^2,x)","-\frac{b \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 \,x^{2}-2 a}{2 \left(4 a c -b^{2}\right) \left(c \,x^{4}+b \,x^{2}+a \right)}"," ",0,"1/2*(-b*x^2-2*a)/(4*a*c-b^2)/(c*x^4+b*x^2+a)-b/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","A"
96,1,342,180,0.069000," ","int(x^4/(c*x^5+b*x^3+a*x)^2,x)","\frac{\sqrt{2}\, 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) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, 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) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{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) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{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) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{x}{2 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}+\frac{x}{2 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}"," ",0,"1/2/(4*a*c-b^2)*x/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/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)+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+1/2/(4*a*c-b^2)*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/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)+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","A"
97,1,75,70,0.006000," ","int(x^3/(c*x^5+b*x^3+a*x)^2,x)","\frac{2 c \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 \,x^{2}+b}{2 \left(4 a c -b^{2}\right) \left(c \,x^{4}+b \,x^{2}+a \right)}"," ",0,"1/2*(2*c*x^2+b)/(4*a*c-b^2)/(c*x^4+b*x^2+a)+2*c/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","A"
98,1,733,206,0.057000," ","int(x^2/(c*x^5+b*x^3+a*x)^2,x)","\frac{\sqrt{2}\, b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \sqrt{2}\, c^{2} \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}}\, \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} \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}}\, \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{b^{2} x}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}-\frac{b^{2} x}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}+\frac{\sqrt{2}\, b 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) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b 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) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{c x}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}+\frac{c x}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{b x}{4 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}-\frac{b x}{4 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}"," ",0,"-1/4/(4*a*c-b^2)/a*x/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*b-c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*x/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)+1/4/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a*x/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*b^2-1/4*c/(4*a*c-b^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)*b-3*c^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)+1/4*c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^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)*b^2-1/4/(4*a*c-b^2)/a*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*b+c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)-1/4/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*b^2+1/4*c/(4*a*c-b^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)*b-3*c^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)+1/4*c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^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)*b^2","B"
99,1,253,112,0.017000," ","int(x/(c*x^5+b*x^3+a*x)^2,x)","-\frac{b c \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{3 b c \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} \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^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a}+\frac{b^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) a^{2}}+\frac{c}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{\ln \left(x \right)}{a^{2}}"," ",0,"1/a^2*ln(x)-1/2/a/(c*x^4+b*x^2+a)*b*c/(4*a*c-b^2)*x^2+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*c-1/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^2-1/a/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)+1/4/a^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^2-3/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*c+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","B"
100,1,712,260,0.034000," ","int(1/(c*x^5+b*x^3+a*x)^2,x)","-\frac{c^{2} x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{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{4 \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(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} \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 \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 \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{3 b c x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{5 \sqrt{2}\, c^{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}\, a}-\frac{5 \sqrt{2}\, c^{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}\, a}+\frac{b^{3} 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 \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 \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{1}{a^{2} x}"," ",0,"-1/a^2/x-1/a/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^3+1/2/a^2/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*b^2-3/2/a/(c*x^4+b*x^2+a)*b*c/(4*a*c-b^2)*x+1/2/a^2/(c*x^4+b*x^2+a)*b^3/(4*a*c-b^2)*x+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)-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+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-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^3-5/2/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)+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+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-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","B"
101,1,352,155,0.020000," ","int(1/x/(c*x^5+b*x^3+a*x)^2,x)","-\frac{c^{2} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{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{6 c^{2} \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 b^{2} c \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} \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 c}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{2 b c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a^{2}}-\frac{b^{3} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(4 a c -b^{2}\right) a^{3}}-\frac{2 b \ln \left(x \right)}{a^{3}}-\frac{1}{2 a^{2} x^{2}}"," ",0,"-1/2/a^2/x^2-2/a^3*b*ln(x)-1/a/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^2+1/2/a^2/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*b^2-3/2/a/(c*x^4+b*x^2+a)*b/(4*a*c-b^2)*c+1/2/a^2/(c*x^4+b*x^2+a)*b^3/(4*a*c-b^2)+2/a^2/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)*b-1/2/a^3/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^3-6/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c^2+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-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","B"
102,1,913,311,0.038000," ","int(1/x^2/(c*x^5+b*x^3+a*x)^2,x)","\frac{3 b \,c^{2} 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 \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{3}}+\frac{7 \sqrt{2}\, 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) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{7 \sqrt{2}\, 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) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{29 \sqrt{2}\, b^{2} c^{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) \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} \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 \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 \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{c^{2} x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{2 b^{2} c x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{19 \sqrt{2}\, b \,c^{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) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{19 \sqrt{2}\, b \,c^{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) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{b^{4} 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 \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 \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{2 b}{a^{3} x}-\frac{1}{3 a^{2} x^{3}}"," ",0,"-1/3/a^2/x^3+2/a^3*b/x+3/2/a^2/(c*x^4+b*x^2+a)*b*c^2/(4*a*c-b^2)*x^3-1/2/a^3/(c*x^4+b*x^2+a)*b^3*c/(4*a*c-b^2)*x^3-1/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*c^2+2/a^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b^2*c-1/2/a^3/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b^4-19/4/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+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+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)-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+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+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-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+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)-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+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","B"
103,1,443,205,0.023000," ","int(1/x^3/(c*x^5+b*x^3+a*x)^2,x)","\frac{3 b \,c^{2} 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 \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{3}}+\frac{15 b \,c^{2} \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{10 b^{3} c \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} \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{c^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{2 b^{2} c}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{2 c^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a^{2}}-\frac{b^{4}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{3}}-\frac{7 b^{2} c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(4 a c -b^{2}\right) a^{3}}+\frac{3 b^{4} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) a^{4}}-\frac{2 c \ln \left(x \right)}{a^{3}}+\frac{3 b^{2} \ln \left(x \right)}{a^{4}}+\frac{b}{a^{3} x^{2}}-\frac{1}{4 a^{2} x^{4}}"," ",0,"-1/4/a^2/x^4-2/a^3*c*ln(x)+3/a^4*b^2*ln(x)+1/a^3*b/x^2+3/2/a^2/(c*x^4+b*x^2+a)*b*c^2/(4*a*c-b^2)*x^2-1/2/a^3/(c*x^4+b*x^2+a)*b^3*c/(4*a*c-b^2)*x^2-1/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*c^2+2/a^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^2*c-1/2/a^3/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^4+2/a^2/(4*a*c-b^2)*c^2*ln(c*x^4+b*x^2+a)-7/2/a^3/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)*b^2+3/4/a^4/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^4+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^2-10/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+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","B"
104,0,0,118,0.040000," ","int(x/(c*x^5+b*x^3+a*x)^(1/2),x)","\int \frac{x}{\sqrt{c \,x^{5}+b \,x^{3}+a x}}\, dx"," ",0,"int(x/(c*x^5+b*x^3+a*x)^(1/2),x)","F"
105,1,1042,364,0.053000," ","int(x^(3/2)*(c*x^5+b*x^3+a*x)^(1/2),x)","-\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \left(-6 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b \,c^{2} x^{7}-6 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, c^{2} x^{7}-8 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{2} c \,x^{5}-8 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b c \,x^{5}-6 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a b c \,x^{3}-2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{3} x^{3}-6 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a c \,x^{3}-2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b^{2} x^{3}-12 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a^{2} c \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)+12 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a^{2} c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a \,b^{2} x +4 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a \,b^{2} \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-3 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a \,b^{2} \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a b x +\sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, \sqrt{-4 a c +b^{2}}\, a b \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)\right)}{30 \left(c \,x^{4}+b \,x^{2}+a \right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \left(b +\sqrt{-4 a c +b^{2}}\right) c \sqrt{x}}"," ",0,"-1/30*(x*(c*x^4+b*x^2+a))^(1/2)*(-6*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^7*b*c^2-6*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^7*c^2-8*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^5*b^2*c-8*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^5*b*c-6*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^3*a*b*c-6*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^3*a*c-2*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^3*b^3-2*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^3*b^2+12*(-2*(x^2*(-4*a*c+b^2)^(1/2)-b*x^2-2*a)/a)^(1/2)*((x^2*(-4*a*c+b^2)^(1/2)+b*x^2+2*a)/a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*(((-4*a*c+b^2)^(1/2)*b-2*a*c+b^2)/a/c)^(1/2))*a^2*c-3*b^2*a*(-2*(x^2*(-4*a*c+b^2)^(1/2)-b*x^2-2*a)/a)^(1/2)*((x^2*(-4*a*c+b^2)^(1/2)+b*x^2+2*a)/a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*(((-4*a*c+b^2)^(1/2)*b-2*a*c+b^2)/a/c)^(1/2))+b*a*(-2*(x^2*(-4*a*c+b^2)^(1/2)-b*x^2-2*a)/a)^(1/2)*((x^2*(-4*a*c+b^2)^(1/2)+b*x^2+2*a)/a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*(((-4*a*c+b^2)^(1/2)*b-2*a*c+b^2)/a/c)^(1/2))*(-4*a*c+b^2)^(1/2)-12*(-2*(x^2*(-4*a*c+b^2)^(1/2)-b*x^2-2*a)/a)^(1/2)*((x^2*(-4*a*c+b^2)^(1/2)+b*x^2+2*a)/a)^(1/2)*EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*(((-4*a*c+b^2)^(1/2)*b-2*a*c+b^2)/a/c)^(1/2))*a^2*c+4*(-2*(x^2*(-4*a*c+b^2)^(1/2)-b*x^2-2*a)/a)^(1/2)*((x^2*(-4*a*c+b^2)^(1/2)+b*x^2+2*a)/a)^(1/2)*EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*(((-4*a*c+b^2)^(1/2)*b-2*a*c+b^2)/a/c)^(1/2))*a*b^2-2*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x*a*b^2-2*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x*a*b)/x^(1/2)/(c*x^4+b*x^2+a)/c/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))","B"
106,1,157,107,0.010000," ","int(x^(1/2)*(c*x^5+b*x^3+a*x)^(1/2),x)","\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \left(4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{\frac{3}{2}} x^{2}+4 a c \ln \left(\frac{2 c \,x^{2}+b +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{c}}{2 \sqrt{c}}\right)-b^{2} \ln \left(\frac{2 c \,x^{2}+b +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{c}}{2 \sqrt{c}}\right)+2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \sqrt{c}\right)}{16 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{\frac{3}{2}} \sqrt{x}}"," ",0,"1/16*((c*x^4+b*x^2+a)*x)^(1/2)/c^(3/2)*(4*x^2*c^(3/2)*(c*x^4+b*x^2+a)^(1/2)+4*ln(1/2*(2*c*x^2+2*(c*x^4+b*x^2+a)^(1/2)*c^(1/2)+b)/c^(1/2))*a*c-ln(1/2*(2*c*x^2+2*(c*x^4+b*x^2+a)^(1/2)*c^(1/2)+b)/c^(1/2))*b^2+2*b*(c*x^4+b*x^2+a)^(1/2)*c^(1/2))/x^(1/2)/(c*x^4+b*x^2+a)^(1/2)","A"
107,1,508,331,0.016000," ","int((c*x^5+b*x^3+a*x)^(1/2)/x^(1/2),x)","\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \left(\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b c \,x^{5}+\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, c \,x^{5}+\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{2} x^{3}+\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b \,x^{3}+\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a b x +\sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a b \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)+\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a x +\sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, \sqrt{-4 a c +b^{2}}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)\right)}{3 \left(c \,x^{4}+b \,x^{2}+a \right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \left(b +\sqrt{-4 a c +b^{2}}\right) \sqrt{x}}"," ",0,"1/3*((c*x^4+b*x^2+a)*x)^(1/2)/x^(1/2)*(((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^5*c+((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^5*b*c+((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^3*b+((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^3*b^2+a*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*(-4*a*c+b^2)^(1/2)+b*a*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))+((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x*a+((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x*a*b)/(c*x^4+b*x^2+a)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))","A"
108,1,136,156,0.013000," ","int((c*x^5+b*x^3+a*x)^(1/2)/x^(3/2),x)","-\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \left(2 \sqrt{a}\, \sqrt{c}\, \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)-b \ln \left(\frac{2 c \,x^{2}+b +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{c}}{2 \sqrt{c}}\right)-2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{c}\right)}{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{c}\, \sqrt{x}}"," ",0,"-1/4*((c*x^4+b*x^2+a)*x)^(1/2)/x^(1/2)*(2*a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)*c^(1/2)-2*(c*x^4+b*x^2+a)^(1/2)*c^(1/2)-b*ln(1/2*(2*c*x^2+b+2*(c*x^4+b*x^2+a)^(1/2)*c^(1/2))/c^(1/2)))/(c*x^4+b*x^2+a)^(1/2)/c^(1/2)","A"
109,1,369,210,0.014000," ","int(x^(3/2)*(c*x^5+b*x^3+a*x)^(3/2),x)","-\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \left(-256 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{\frac{9}{2}} x^{8}-352 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,c^{\frac{7}{2}} x^{6}-512 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,c^{\frac{7}{2}} x^{4}-16 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} c^{\frac{5}{2}} x^{4}-112 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a b \,c^{\frac{5}{2}} x^{2}+20 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3} c^{\frac{3}{2}} x^{2}+240 a^{2} b \,c^{2} \ln \left(\frac{2 c \,x^{2}+b +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{c}}{2 \sqrt{c}}\right)-120 a \,b^{3} c \ln \left(\frac{2 c \,x^{2}+b +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{c}}{2 \sqrt{c}}\right)+15 b^{5} \ln \left(\frac{2 c \,x^{2}+b +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{c}}{2 \sqrt{c}}\right)-256 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2} c^{\frac{5}{2}}+200 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,b^{2} c^{\frac{3}{2}}-30 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{4} \sqrt{c}\right)}{2560 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{\frac{7}{2}} \sqrt{x}}"," ",0,"-1/2560*((c*x^4+b*x^2+a)*x)^(1/2)/c^(7/2)*(-256*x^8*c^(9/2)*(c*x^4+b*x^2+a)^(1/2)-352*x^6*b*c^(7/2)*(c*x^4+b*x^2+a)^(1/2)-512*x^4*a*c^(7/2)*(c*x^4+b*x^2+a)^(1/2)-16*x^4*b^2*c^(5/2)*(c*x^4+b*x^2+a)^(1/2)-112*x^2*a*b*c^(5/2)*(c*x^4+b*x^2+a)^(1/2)+20*x^2*b^3*c^(3/2)*(c*x^4+b*x^2+a)^(1/2)+240*ln(1/2*(2*c*x^2+b+2*(c*x^4+b*x^2+a)^(1/2)*c^(1/2))/c^(1/2))*a^2*b*c^2-120*ln(1/2*(2*c*x^2+b+2*(c*x^4+b*x^2+a)^(1/2)*c^(1/2))/c^(1/2))*a*b^3*c+15*ln(1/2*(2*c*x^2+b+2*(c*x^4+b*x^2+a)^(1/2)*c^(1/2))/c^(1/2))*b^5-256*a^2*c^(5/2)*(c*x^4+b*x^2+a)^(1/2)+200*a*b^2*c^(3/2)*(c*x^4+b*x^2+a)^(1/2)-30*b^4*c^(1/2)*(c*x^4+b*x^2+a)^(1/2))/x^(1/2)/(c*x^4+b*x^2+a)^(1/2)","A"
110,1,1878,465,0.020000," ","int((c*x^5+b*x^3+a*x)^(3/2)*x^(1/2),x)","-\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \left(-35 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b \,c^{4} x^{11}-35 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, c^{4} x^{11}-85 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{2} c^{3} x^{9}-85 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b \,c^{3} x^{9}-112 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a b \,c^{3} x^{7}-53 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{3} c^{2} x^{7}-112 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a \,c^{3} x^{7}-53 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b^{2} c^{2} x^{7}-151 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a \,b^{2} c^{2} x^{5}+\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{4} c \,x^{5}-151 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a b \,c^{2} x^{5}+\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b^{3} c \,x^{5}-77 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a^{2} b \,c^{2} x^{3}-27 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a \,b^{3} c \,x^{3}+4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{5} x^{3}-77 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a^{2} c^{2} x^{3}-27 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{2} c \,x^{3}+4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b^{4} x^{3}-84 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a^{3} c^{2} \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)+84 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a^{3} c^{2} \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-24 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a^{2} b^{2} c x +57 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a^{2} b^{2} c \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-45 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a^{2} b^{2} c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)+4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a \,b^{4} x -8 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a \,b^{4} \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)+6 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a \,b^{4} \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-24 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a^{2} b c x +12 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, \sqrt{-4 a c +b^{2}}\, a^{2} b c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)+4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{3} x -2 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{3} \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)\right)}{315 \left(c \,x^{4}+b \,x^{2}+a \right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \left(b +\sqrt{-4 a c +b^{2}}\right) c^{2} \sqrt{x}}"," ",0,"-1/315*((c*x^4+b*x^2+a)*x)^(1/2)/x^(1/2)*(-85*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^9*b*c^3-2*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*(-4*a*c+b^2)^(1/2)*a*b^3-35*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^11*c^4-35*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^11*b*c^4-85*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^9*b^2*c^3-53*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^7*b^3*c^2+((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^5*b^4*c+4*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^3*b^4+4*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x*a*b^4+4*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^3*b^5-45*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*a^2*b^2*c+57*EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*a^2*b^2*c-151*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^5*a*b*c^2-27*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^3*a*b^2*c-24*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x*a^2*b*c+12*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*(-4*a*c+b^2)^(1/2)*a^2*b*c-112*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^7*a*c^3-53*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^7*b^2*c^2-112*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^7*a*b*c^3+((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^5*b^3*c-151*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^5*a*b^2*c^2-77*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^3*a^2*c^2-77*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^3*a^2*b*c^2+84*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*a^3*c^2+6*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*a*b^4-84*EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*a^3*c^2-8*EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*a*b^4+4*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x*a*b^3-24*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x*a^2*b^2*c-27*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^3*a*b^3*c)/(c*x^4+b*x^2+a)/c^2/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))","B"
111,1,295,149,0.023000," ","int((c*x^5+b*x^3+a*x)^(3/2)/x^(1/2),x)","\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \left(32 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{\frac{7}{2}} x^{6}+48 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,c^{\frac{5}{2}} x^{4}+80 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,c^{\frac{5}{2}} x^{2}+4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} c^{\frac{3}{2}} x^{2}+48 a^{2} c^{2} \ln \left(\frac{2 c \,x^{2}+b +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{c}}{2 \sqrt{c}}\right)-24 a \,b^{2} c \ln \left(\frac{2 c \,x^{2}+b +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{c}}{2 \sqrt{c}}\right)+3 b^{4} \ln \left(\frac{2 c \,x^{2}+b +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{c}}{2 \sqrt{c}}\right)+40 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a b \,c^{\frac{3}{2}}-6 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3} \sqrt{c}\right)}{256 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{\frac{5}{2}} \sqrt{x}}"," ",0,"1/256*((c*x^4+b*x^2+a)*x)^(1/2)/c^(5/2)*(32*x^6*c^(7/2)*(c*x^4+b*x^2+a)^(1/2)+48*x^4*b*c^(5/2)*(c*x^4+b*x^2+a)^(1/2)+80*x^2*a*c^(5/2)*(c*x^4+b*x^2+a)^(1/2)+4*x^2*b^2*c^(3/2)*(c*x^4+b*x^2+a)^(1/2)+48*ln(1/2*(2*c*x^2+b+2*(c*x^4+b*x^2+a)^(1/2)*c^(1/2))/c^(1/2))*a^2*c^2-24*ln(1/2*(2*c*x^2+b+2*(c*x^4+b*x^2+a)^(1/2)*c^(1/2))/c^(1/2))*a*b^2*c+3*ln(1/2*(2*c*x^2+b+2*(c*x^4+b*x^2+a)^(1/2)*c^(1/2))/c^(1/2))*b^4+40*a*b*c^(3/2)*(c*x^4+b*x^2+a)^(1/2)-6*b^3*c^(1/2)*(c*x^4+b*x^2+a)^(1/2))/x^(1/2)/(c*x^4+b*x^2+a)^(1/2)","A"
112,1,1394,403,0.020000," ","int((c*x^5+b*x^3+a*x)^(3/2)/x^(3/2),x)","-\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \left(-10 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b \,c^{3} x^{9}-10 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, c^{3} x^{9}-26 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{2} c^{2} x^{7}-26 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b \,c^{2} x^{7}-40 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a b \,c^{2} x^{5}-18 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{3} c \,x^{5}-40 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a \,c^{2} x^{5}-18 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b^{2} c \,x^{5}-46 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a \,b^{2} c \,x^{3}-2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{4} x^{3}-46 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a b c \,x^{3}-2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b^{3} x^{3}-30 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a^{2} b c x -32 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a^{2} b c \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)+12 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a^{2} b c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a \,b^{3} x +4 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a \,b^{3} \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-3 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a \,b^{3} \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-30 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a^{2} c x -20 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, \sqrt{-4 a c +b^{2}}\, a^{2} c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{2} x +\sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{2} \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)\right)}{70 \left(c \,x^{4}+b \,x^{2}+a \right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \left(b +\sqrt{-4 a c +b^{2}}\right) c \sqrt{x}}"," ",0,"-1/70*((c*x^4+b*x^2+a)*x)^(1/2)*(-10*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^9*b*c^3-10*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^9*c^3-26*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^7*b^2*c^2-26*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^7*b*c^2-40*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^5*a*b*c^2-40*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^5*a*c^2-18*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^5*b^3*c-18*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^5*b^2*c-46*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^3*a*b^2*c-46*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^3*a*b*c-2*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^3*b^4-2*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^3*b^3+12*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*a^2*b*c-20*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*(-4*a*c+b^2)^(1/2)*a^2*c-3*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*a*b^3+(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*(-4*a*c+b^2)^(1/2)*a*b^2-32*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*a^2*b*c+4*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*a*b^3-30*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x*a^2*b*c-30*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x*a^2*c-2*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x*a*b^3-2*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x*a*b^2)/x^(1/2)/(c*x^4+b*x^2+a)/c/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))","B"
113,1,72,66,0.011000," ","int(x^(3/2)/(c*x^5+b*x^3+a*x)^(1/2),x)","\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \ln \left(\frac{2 c \,x^{2}+b +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{c}}{2 \sqrt{c}}\right)}{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{c}\, \sqrt{x}}"," ",0,"1/2/x^(1/2)*((c*x^4+b*x^2+a)*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*ln(1/2*(2*c*x^2+b+2*(c*x^4+b*x^2+a)^(1/2)*c^(1/2))/c^(1/2))/c^(1/2)","A"
114,1,177,124,0.015000," ","int(x^(1/2)/(c*x^5+b*x^3+a*x)^(1/2),x)","\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{x}}"," ",0,"1/2/x^(1/2)*((c*x^4+b*x^2+a)*x)^(1/2)/(c*x^4+b*x^2+a)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))","A"
115,1,72,39,0.018000," ","int(1/x^(1/2)/(c*x^5+b*x^3+a*x)^(1/2),x)","-\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}\, \sqrt{x}}"," ",0,"-1/2/x^(1/2)*((c*x^4+b*x^2+a)*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
116,1,508,324,0.018000," ","int(1/x^(3/2)/(c*x^5+b*x^3+a*x)^(1/2),x)","\frac{\left(-\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b c \,x^{4}-\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, c \,x^{4}+\sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a c x \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-\sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a c x \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{2} x^{2}-\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b \,x^{2}-\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a b -\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a \right) \sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}}{\left(c \,x^{4}+b \,x^{2}+a \right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \left(b +\sqrt{-4 a c +b^{2}}\right) a \,x^{\frac{3}{2}}}"," ",0,"(-((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^4*c-((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^4*b*c-c*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*a*x*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))+c*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*a*x*EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))-((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^2*b-((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^2*b^2-((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*a-((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*a*b)/x^(3/2)*((c*x^4+b*x^2+a)*x)^(1/2)/(c*x^4+b*x^2+a)/a/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))","A"
117,1,533,381,0.019000," ","int(x^(3/2)/(c*x^5+b*x^3+a*x)^(3/2),x)","\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \left(-\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{2} c \,x^{3}-\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b c \,x^{3}+2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a b c x +\sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a b c \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{3} x +2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a c x +\sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, \sqrt{-4 a c +b^{2}}\, a c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b^{2} x \right)}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \left(b +\sqrt{-4 a c +b^{2}}\right) a \sqrt{x}}"," ",0,"((c*x^4+b*x^2+a)*x)^(1/2)*(-((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^3*b^2*c-((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^3*b*c+c*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*a*(-4*a*c+b^2)^(1/2)+b*c*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*a*EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))+2*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x*a*b*c+2*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x*a*c-((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x*b^3-((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x*b^2)/x^(1/2)/(c*x^4+b*x^2+a)/a/(4*a*c-b^2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))","A"
118,1,179,87,0.015000," ","int(x^(1/2)/(c*x^5+b*x^3+a*x)^(3/2),x)","-\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \left(2 \sqrt{a}\, b c \,x^{2}+4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)-\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)-4 a^{\frac{3}{2}} c +2 \sqrt{a}\, b^{2}\right)}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{\frac{3}{2}} \sqrt{x}}"," ",0,"-1/2*((c*x^4+b*x^2+a)*x)^(1/2)/a^(3/2)*(2*x^2*b*c*a^(1/2)+4*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)*a*c*(c*x^4+b*x^2+a)^(1/2)-ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)*b^2*(c*x^4+b*x^2+a)^(1/2)-4*a^(3/2)*c+2*b^2*a^(1/2))/x^(1/2)/(c*x^4+b*x^2+a)/(4*a*c-b^2)","B"
119,1,1136,454,0.045000," ","int(1/(c*x^5+b*x^3+a*x)^(3/2)/x^(1/2),x)","-\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \left(12 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a b \,c^{2} x^{4}-4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{3} c \,x^{4}+12 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a \,c^{2} x^{4}-4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b^{2} c \,x^{4}-12 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a^{2} c^{2} x \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)+12 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a^{2} c^{2} x \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)+14 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a \,b^{2} c \,x^{2}+4 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a \,b^{2} c x \EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-3 \sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, a \,b^{2} c x \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, b^{4} x^{2}+14 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a b c \,x^{2}+\sqrt{-\frac{2 \left(-b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}-2 a \right)}{a}}\, \sqrt{\frac{b \,x^{2}+\sqrt{-4 a c +b^{2}}\, x^{2}+2 a}{a}}\, \sqrt{-4 a c +b^{2}}\, a b c x \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{2}\, \sqrt{\frac{-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{a c}}}{2}\right)-4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, b^{3} x^{2}+8 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a^{2} b c -2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, a \,b^{3}+8 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a^{2} c -2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{-4 a c +b^{2}}\, a \,b^{2}\right)}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \left(b +\sqrt{-4 a c +b^{2}}\right) a^{2} x^{\frac{3}{2}}}"," ",0,"-1/2*((c*x^4+b*x^2+a)*x)^(1/2)/x^(3/2)*(12*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^4*a*c^2-4*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^4*b^2*c+12*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^4*a*b*c^2-4*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^4*b^3*c+a*b*c*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*x*(-4*a*c+b^2)^(1/2)+12*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*x*a^2*c^2-3*a*b^2*c*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*x-12*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*x*a^2*c^2+4*(-2*(-b*x^2+(-4*a*c+b^2)^(1/2)*x^2-2*a)/a)^(1/2)*((b*x^2+(-4*a*c+b^2)^(1/2)*x^2+2*a)/a)^(1/2)*EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*2^(1/2)*((-2*a*c+b^2+(-4*a*c+b^2)^(1/2)*b)/a/c)^(1/2))*x*a*b^2*c+14*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^2*a*b*c-4*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*x^2*b^3+14*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^2*a*b^2*c-4*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x^2*b^4+8*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*a^2*c-2*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-4*a*c+b^2)^(1/2)*a*b^2+8*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*a^2*b*c-2*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*a*b^3)/(c*x^4+b*x^2+a)/a^2/(4*a*c-b^2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))","B"
120,1,220,132,0.023000," ","int(1/x^(3/2)/(c*x^5+b*x^3+a*x)^(3/2),x)","\frac{\sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \left(-16 a^{\frac{3}{2}} c^{2} x^{4}+6 \sqrt{a}\, b^{2} c \,x^{4}+12 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a b c \,x^{2} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)-3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3} x^{2} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)-20 a^{\frac{3}{2}} b c \,x^{2}+6 \sqrt{a}\, b^{3} x^{2}-8 a^{\frac{5}{2}} c +2 a^{\frac{3}{2}} b^{2}\right)}{4 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{\frac{5}{2}} x^{\frac{5}{2}}}"," ",0,"1/4*((c*x^4+b*x^2+a)*x)^(1/2)/a^(5/2)*(-16*x^4*a^(3/2)*c^2+6*x^4*b^2*c*a^(1/2)+12*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)*x^2*a*b*c*(c*x^4+b*x^2+a)^(1/2)-3*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)*x^2*b^3*(c*x^4+b*x^2+a)^(1/2)-20*a^(3/2)*x^2*b*c+6*x^2*b^3*a^(1/2)-8*a^(5/2)*c+2*a^(3/2)*b^2)/x^(5/2)/(c*x^4+b*x^2+a)/(4*a*c-b^2)","A"
121,0,0,47,0.079000," ","int(x^(3/2*n-3/2)/(a*x^(n-1)+b*x^n+c*x^(n+1))^(3/2),x)","\int \frac{x^{\frac{3 n}{2}-\frac{3}{2}}}{\left(a \,x^{n -1}+b \,x^{n}+c \,x^{n +1}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^(3/2*n-3/2)/(a*x^(n-1)+b*x^n+c*x^(n+1))^(3/2),x)","F"
122,0,0,239,0.038000," ","int(x*(e*x^2+d)/(c*x^5+b*x^3+a*x)^(1/2),x)","\int \frac{\left(e \,x^{2}+d \right) x}{\sqrt{c \,x^{5}+b \,x^{3}+a x}}\, dx"," ",0,"int(x*(e*x^2+d)/(c*x^5+b*x^3+a*x)^(1/2),x)","F"
123,1,58,35,0.011000," ","int(1/(x^6-3*x^4+3*x^2)^(1/2),x)","\frac{\sqrt{x^{4}-3 x^{2}+3}\, \sqrt{3}\, x \arctanh \left(\frac{\left(x^{2}-2\right) \sqrt{3}}{2 \sqrt{x^{4}-3 x^{2}+3}}\right)}{6 \sqrt{x^{6}-3 x^{4}+3 x^{2}}}"," ",0,"1/6/(x^6-3*x^4+3*x^2)^(1/2)*x*(x^4-3*x^2+3)^(1/2)*3^(1/2)*arctanh(1/2*(x^2-2)*3^(1/2)/(x^4-3*x^2+3)^(1/2))","A"
124,1,58,35,0.007000," ","int(1/(x^2*(x^4-3*x^2+3))^(1/2),x)","\frac{\sqrt{x^{4}-3 x^{2}+3}\, \sqrt{3}\, x \arctanh \left(\frac{\left(x^{2}-2\right) \sqrt{3}}{2 \sqrt{x^{4}-3 x^{2}+3}}\right)}{6 \sqrt{\left(x^{4}-3 x^{2}+3\right) x^{2}}}"," ",0,"1/6/(x^2*(x^4-3*x^2+3))^(1/2)*x*(x^4-3*x^2+3)^(1/2)*3^(1/2)*arctanh(1/2*(x^2-2)*3^(1/2)/(x^4-3*x^2+3)^(1/2))","A"
125,1,58,35,0.004000," ","int(1/(1-(-x^2+1)^3)^(1/2),x)","\frac{\sqrt{x^{4}-3 x^{2}+3}\, \sqrt{3}\, x \arctanh \left(\frac{\left(x^{2}-2\right) \sqrt{3}}{2 \sqrt{x^{4}-3 x^{2}+3}}\right)}{6 \sqrt{x^{6}-3 x^{4}+3 x^{2}}}"," ",0,"1/6/(x^6-3*x^4+3*x^2)^(1/2)*x*(x^4-3*x^2+3)^(1/2)*3^(1/2)*arctanh(1/2*(x^2-2)*3^(1/2)/(x^4-3*x^2+3)^(1/2))","A"
126,1,81,75,0.010000," ","int((x^6-3*x^4+3*x^2)^(1/2),x)","\frac{\sqrt{x^{6}-3 x^{4}+3 x^{2}}\, \left(4 \sqrt{x^{4}-3 x^{2}+3}\, x^{2}+3 \arcsinh \left(\frac{\sqrt{3}\, \left(2 x^{2}-3\right)}{3}\right)-6 \sqrt{x^{4}-3 x^{2}+3}\right)}{16 \sqrt{x^{4}-3 x^{2}+3}\, x}"," ",0,"1/16*(x^6-3*x^4+3*x^2)^(1/2)*(4*(x^4-3*x^2+3)^(1/2)*x^2+3*arcsinh(1/3*3^(1/2)*(2*x^2-3))-6*(x^4-3*x^2+3)^(1/2))/x/(x^4-3*x^2+3)^(1/2)","A"
127,1,81,75,0.006000," ","int(((x^4-3*x^2+3)*x^2)^(1/2),x)","\frac{\sqrt{\left(x^{4}-3 x^{2}+3\right) x^{2}}\, \left(4 \sqrt{x^{4}-3 x^{2}+3}\, x^{2}+3 \arcsinh \left(\frac{\sqrt{3}\, \left(2 x^{2}-3\right)}{3}\right)-6 \sqrt{x^{4}-3 x^{2}+3}\right)}{16 \sqrt{x^{4}-3 x^{2}+3}\, x}"," ",0,"1/16*((x^4-3*x^2+3)*x^2)^(1/2)*(4*(x^4-3*x^2+3)^(1/2)*x^2+3*arcsinh(1/3*3^(1/2)*(2*x^2-3))-6*(x^4-3*x^2+3)^(1/2))/x/(x^4-3*x^2+3)^(1/2)","A"
128,1,81,75,0.004000," ","int((1-(-x^2+1)^3)^(1/2),x)","\frac{\sqrt{x^{6}-3 x^{4}+3 x^{2}}\, \left(4 \sqrt{x^{4}-3 x^{2}+3}\, x^{2}+3 \arcsinh \left(\frac{\sqrt{3}\, \left(2 x^{2}-3\right)}{3}\right)-6 \sqrt{x^{4}-3 x^{2}+3}\right)}{16 \sqrt{x^{4}-3 x^{2}+3}\, x}"," ",0,"1/16*(x^6-3*x^4+3*x^2)^(1/2)*(4*(x^4-3*x^2+3)^(1/2)*x^2+3*arcsinh(1/3*3^(1/2)*(2*x^2-3))-6*(x^4-3*x^2+3)^(1/2))/x/(x^4-3*x^2+3)^(1/2)","A"
129,1,35,30,0.003000," ","int(1/x/(c*x^2+b*x+a)^(1/2),x)","-\frac{\ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\sqrt{a}}"," ",0,"-1/a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)","A"
130,1,64,37,0.009000," ","int(1/(x^2*(c*x^2+b*x+a))^(1/2),x)","-\frac{\sqrt{c \,x^{2}+b x +a}\, x \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\sqrt{\left(c \,x^{2}+b x +a \right) x^{2}}\, \sqrt{a}}"," ",0,"-1/(x^2*(c*x^2+b*x+a))^(1/2)*x*(c*x^2+b*x+a)^(1/2)/a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)","A"
131,1,64,37,0.014000," ","int(1/x^(1/2)/(x*(c*x^2+b*x+a))^(1/2),x)","-\frac{\sqrt{c \,x^{2}+b x +a}\, \sqrt{x}\, \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\sqrt{\left(c \,x^{2}+b x +a \right) x}\, \sqrt{a}}"," ",0,"-x^(1/2)/(x*(c*x^2+b*x+a))^(1/2)*(c*x^2+b*x+a)^(1/2)/a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)","A"
132,1,66,39,0.008000," ","int(x^(1/2)/(x^3*(c*x^2+b*x+a))^(1/2),x)","-\frac{\sqrt{c \,x^{2}+b x +a}\, x^{\frac{3}{2}} \ln \left(\frac{b x +2 a +2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{a}}{x}\right)}{\sqrt{\left(c \,x^{2}+b x +a \right) x^{3}}\, \sqrt{a}}"," ",0,"-1/(x^3*(c*x^2+b*x+a))^(1/2)*x^(3/2)*(c*x^2+b*x+a)^(1/2)/a^(1/2)*ln((b*x+2*a+2*(c*x^2+b*x+a)^(1/2)*a^(1/2))/x)","A"
133,1,39,34,0.006000," ","int(1/x/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{\ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2 \sqrt{a}}"," ",0,"-1/2/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
134,1,72,39,0.007000," ","int(1/(x^2*(c*x^4+b*x^2+a))^(1/2),x)","-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2 \sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x^{2}}\, \sqrt{a}}"," ",0,"-1/2/(x^2*(c*x^4+b*x^2+a))^(1/2)*x*(c*x^4+b*x^2+a)^(1/2)/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
135,1,72,39,0.011000," ","int(1/x^(1/2)/((c*x^4+b*x^2+a)*x)^(1/2),x)","-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{x}\, \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2 \sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, \sqrt{a}}"," ",0,"-1/2*x^(1/2)/((c*x^4+b*x^2+a)*x)^(1/2)*(c*x^4+b*x^2+a)^(1/2)/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
136,1,74,41,0.010000," ","int(x^(1/2)/(x^3*(c*x^4+b*x^2+a))^(1/2),x)","-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{\frac{3}{2}} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2 \sqrt{\left(c \,x^{4}+b \,x^{2}+a \right) x^{3}}\, \sqrt{a}}"," ",0,"-1/2/(x^3*(c*x^4+b*x^2+a))^(1/2)*x^(3/2)*(c*x^4+b*x^2+a)^(1/2)/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
137,1,31,30,0.004000," ","int(1/x/(x^4-3*x^2+3)^(1/2),x)","-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(-3 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}-3 x^{2}+3}}\right)}{6}"," ",0,"-1/6*3^(1/2)*arctanh(1/6*(-3*x^2+6)*3^(1/2)/(x^4-3*x^2+3)^(1/2))","A"
138,1,58,35,0.000000," ","int(1/((x^4-3*x^2+3)*x^2)^(1/2),x)","\frac{\sqrt{x^{4}-3 x^{2}+3}\, \sqrt{3}\, x \arctanh \left(\frac{\left(x^{2}-2\right) \sqrt{3}}{2 \sqrt{x^{4}-3 x^{2}+3}}\right)}{6 \sqrt{\left(x^{4}-3 x^{2}+3\right) x^{2}}}"," ",0,"1/6/((x^4-3*x^2+3)*x^2)^(1/2)*x*(x^4-3*x^2+3)^(1/2)*3^(1/2)*arctanh(1/2*(x^2-2)*3^(1/2)/(x^4-3*x^2+3)^(1/2))","A"
139,1,50,33,0.013000," ","int(1/x^(1/2)/(x*(x^2-3*x+3))^(1/2),x)","\frac{\sqrt{x^{2}-3 x +3}\, \sqrt{3}\, \sqrt{x}\, \arctanh \left(\frac{\left(x -2\right) \sqrt{3}}{2 \sqrt{x^{2}-3 x +3}}\right)}{3 \sqrt{\left(x^{2}-3 x +3\right) x}}"," ",0,"1/3*x^(1/2)/(x*(x^2-3*x+3))^(1/2)*(x^2-3*x+3)^(1/2)*3^(1/2)*arctanh(1/2*(x-2)*3^(1/2)/(x^2-3*x+3)^(1/2))","A"
140,0,0,60,0.138000," ","int(x^(-1+1/2*q)/(b*x^n+c*x^(2*n-q)+a*x^q)^(1/2),x)","\int \frac{x^{\frac{q}{2}-1}}{\sqrt{a \,x^{q}+b \,x^{n}+c \,x^{2 n -q}}}\, dx"," ",0,"int(x^(-1+1/2*q)/(b*x^n+c*x^(2*n-q)+a*x^q)^(1/2),x)","F"