1,1,126,125,0.010000," ","int(x^3*(e*x^2+d)*(c*x^4+a)^5,x)","\frac{1}{26} c^{5} e \,x^{26}+\frac{1}{24} c^{5} d \,x^{24}+\frac{5}{22} a \,c^{4} e \,x^{22}+\frac{1}{4} a \,c^{4} d \,x^{20}+\frac{5}{9} a^{2} c^{3} e \,x^{18}+\frac{5}{8} a^{2} c^{3} d \,x^{16}+\frac{5}{7} a^{3} c^{2} e \,x^{14}+\frac{5}{6} a^{3} c^{2} d \,x^{12}+\frac{1}{2} a^{4} c e \,x^{10}+\frac{5}{8} a^{4} c d \,x^{8}+\frac{1}{6} a^{5} e \,x^{6}+\frac{1}{4} a^{5} d \,x^{4}"," ",0,"1/4*a^5*d*x^4+1/6*a^5*e*x^6+5/8*a^4*c*d*x^8+1/2*a^4*c*e*x^10+5/6*a^3*c^2*d*x^12+5/7*a^3*c^2*e*x^14+5/8*a^2*c^3*d*x^16+5/9*a^2*c^3*e*x^18+1/4*a*c^4*d*x^20+5/22*a*c^4*e*x^22+1/24*c^5*d*x^24+1/26*c^5*e*x^26","A"
2,1,126,125,0.000000," ","int(x^2*(e*x^2+d)*(c*x^4+a)^5,x)","\frac{1}{25} c^{5} e \,x^{25}+\frac{1}{23} c^{5} d \,x^{23}+\frac{5}{21} a \,c^{4} e \,x^{21}+\frac{5}{19} a \,c^{4} d \,x^{19}+\frac{10}{17} a^{2} c^{3} e \,x^{17}+\frac{2}{3} a^{2} c^{3} d \,x^{15}+\frac{10}{13} a^{3} c^{2} e \,x^{13}+\frac{10}{11} a^{3} c^{2} d \,x^{11}+\frac{5}{9} a^{4} c e \,x^{9}+\frac{5}{7} a^{4} c d \,x^{7}+\frac{1}{5} a^{5} e \,x^{5}+\frac{1}{3} a^{5} d \,x^{3}"," ",0,"1/3*a^5*d*x^3+1/5*a^5*e*x^5+5/7*a^4*c*d*x^7+5/9*a^4*c*e*x^9+10/11*a^3*c^2*d*x^11+10/13*a^3*c^2*e*x^13+2/3*a^2*c^3*d*x^15+10/17*a^2*c^3*e*x^17+5/19*a*c^4*d*x^19+5/21*a*c^4*e*x^21+1/23*c^5*d*x^23+1/25*c^5*e*x^25","A"
3,1,125,77,0.003000," ","int(x*(e*x^2+d)*(c*x^4+a)^5,x)","\frac{1}{24} c^{5} e \,x^{24}+\frac{1}{22} c^{5} d \,x^{22}+\frac{1}{4} a \,c^{4} e \,x^{20}+\frac{5}{18} a \,c^{4} d \,x^{18}+\frac{5}{8} a^{2} c^{3} e \,x^{16}+\frac{5}{7} a^{2} c^{3} d \,x^{14}+\frac{5}{6} a^{3} c^{2} e \,x^{12}+a^{3} c^{2} d \,x^{10}+\frac{5}{8} a^{4} c e \,x^{8}+\frac{5}{6} a^{4} c d \,x^{6}+\frac{1}{4} a^{5} e \,x^{4}+\frac{1}{2} a^{5} d \,x^{2}"," ",0,"1/24*c^5*e*x^24+1/22*c^5*d*x^22+1/4*a*c^4*e*x^20+5/18*a*c^4*d*x^18+5/8*a^2*c^3*e*x^16+5/7*a^2*c^3*d*x^14+5/6*a^3*c^2*e*x^12+a^3*c^2*d*x^10+5/8*a^4*c*e*x^8+5/6*a^4*c*d*x^6+1/4*a^5*e*x^4+1/2*a^5*d*x^2","A"
4,1,122,121,0.001000," ","int((e*x^2+d)*(c*x^4+a)^5,x)","\frac{1}{23} c^{5} e \,x^{23}+\frac{1}{21} c^{5} d \,x^{21}+\frac{5}{19} a \,c^{4} e \,x^{19}+\frac{5}{17} a \,c^{4} d \,x^{17}+\frac{2}{3} a^{2} c^{3} e \,x^{15}+\frac{10}{13} a^{2} c^{3} d \,x^{13}+\frac{10}{11} a^{3} c^{2} e \,x^{11}+\frac{10}{9} a^{3} c^{2} d \,x^{9}+\frac{5}{7} a^{4} c e \,x^{7}+a^{4} c d \,x^{5}+\frac{1}{3} a^{5} e \,x^{3}+a^{5} d x"," ",0,"a^5*d*x+1/3*a^5*e*x^3+a^4*c*d*x^5+5/7*a^4*c*e*x^7+10/9*a^3*c^2*d*x^9+10/11*a^3*c^2*e*x^11+10/13*a^2*c^3*d*x^13+2/3*a^2*c^3*e*x^15+5/17*a*c^4*d*x^17+5/19*a*c^4*e*x^19+1/21*c^5*d*x^21+1/23*c^5*e*x^23","A"
5,1,123,122,0.014000," ","int((e*x^2+d)*(c*x^4+a)^5/x,x)","\frac{c^{5} e \,x^{22}}{22}+\frac{c^{5} d \,x^{20}}{20}+\frac{5 a \,c^{4} e \,x^{18}}{18}+\frac{5 a \,c^{4} d \,x^{16}}{16}+\frac{5 a^{2} c^{3} e \,x^{14}}{7}+\frac{5 a^{2} c^{3} d \,x^{12}}{6}+a^{3} c^{2} e \,x^{10}+\frac{5 a^{3} c^{2} d \,x^{8}}{4}+\frac{5 a^{4} c e \,x^{6}}{6}+\frac{5 a^{4} c d \,x^{4}}{4}+\frac{a^{5} e \,x^{2}}{2}+a^{5} d \ln \left(x \right)"," ",0,"1/2*a^5*e*x^2+5/4*a^4*c*d*x^4+5/6*a^4*c*e*x^6+5/4*a^3*c^2*d*x^8+a^3*c^2*e*x^10+5/6*a^2*c^3*d*x^12+5/7*a^2*c^3*e*x^14+5/16*a*c^4*d*x^16+5/18*a*c^4*e*x^18+1/20*c^5*d*x^20+1/22*c^5*e*x^22+a^5*d*ln(x)","A"
6,1,122,121,0.017000," ","int((e*x^2+d)*(c*x^4+a)^5/x^2,x)","\frac{c^{5} e \,x^{21}}{21}+\frac{c^{5} d \,x^{19}}{19}+\frac{5 a \,c^{4} e \,x^{17}}{17}+\frac{a \,c^{4} d \,x^{15}}{3}+\frac{10 a^{2} c^{3} e \,x^{13}}{13}+\frac{10 a^{2} c^{3} d \,x^{11}}{11}+\frac{10 a^{3} c^{2} e \,x^{9}}{9}+\frac{10 a^{3} c^{2} d \,x^{7}}{7}+a^{4} c e \,x^{5}+\frac{5 a^{4} c d \,x^{3}}{3}+a^{5} e x -\frac{a^{5} d}{x}"," ",0,"-a^5*d/x+a^5*e*x+5/3*a^4*c*d*x^3+a^4*c*e*x^5+10/7*a^3*c^2*d*x^7+10/9*a^3*c^2*e*x^9+10/11*a^2*c^3*d*x^11+10/13*a^2*c^3*e*x^13+1/3*a*c^4*d*x^15+5/17*a*c^4*e*x^17+1/19*c^5*d*x^19+1/21*c^5*e*x^21","A"
7,1,123,122,0.009000," ","int((e*x^2+d)*(c*x^4+a)^5/x^3,x)","\frac{c^{5} e \,x^{20}}{20}+\frac{c^{5} d \,x^{18}}{18}+\frac{5 a \,c^{4} e \,x^{16}}{16}+\frac{5 a \,c^{4} d \,x^{14}}{14}+\frac{5 a^{2} c^{3} e \,x^{12}}{6}+a^{2} c^{3} d \,x^{10}+\frac{5 a^{3} c^{2} e \,x^{8}}{4}+\frac{5 a^{3} c^{2} d \,x^{6}}{3}+\frac{5 a^{4} c e \,x^{4}}{4}+\frac{5 a^{4} c d \,x^{2}}{2}+a^{5} e \ln \left(x \right)-\frac{a^{5} d}{2 x^{2}}"," ",0,"-1/2*a^5*d/x^2+5/2*a^4*c*d*x^2+5/4*a^4*c*e*x^4+5/3*a^3*c^2*d*x^6+5/4*a^3*c^2*e*x^8+a^2*c^3*d*x^10+5/6*a^2*c^3*e*x^12+5/14*a*c^4*d*x^14+5/16*a*c^4*e*x^16+1/18*c^5*d*x^18+1/20*c^5*e*x^20+a^5*e*ln(x)","A"
8,1,53,52,0.046000," ","int(x^5*(3*x^2+2)*(x^4+5)^(1/2),x)","\frac{\left(x^{4}+5\right)^{\frac{3}{2}} x^{2}}{4}-\frac{5 \sqrt{x^{4}+5}\, x^{2}}{8}-\frac{25 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{8}+\frac{\left(x^{4}+5\right)^{\frac{3}{2}} \left(3 x^{4}-10\right)}{10}"," ",0,"1/10*(x^4+5)^(3/2)*(3*x^4-10)+1/4*x^2*(x^4+5)^(3/2)-5/8*x^2*(x^4+5)^(1/2)-25/8*arcsinh(1/5*x^2*5^(1/2))","A"
9,1,46,40,0.006000," ","int(x^3*(3*x^2+2)*(x^4+5)^(1/2),x)","\frac{3 \left(x^{4}+5\right)^{\frac{3}{2}} x^{2}}{8}-\frac{15 \sqrt{x^{4}+5}\, x^{2}}{16}-\frac{75 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{16}+\frac{\left(x^{4}+5\right)^{\frac{3}{2}}}{3}"," ",0,"3/8*(x^4+5)^(3/2)*x^2-15/16*(x^4+5)^(1/2)*x^2-75/16*arcsinh(1/5*5^(1/2)*x^2)+1/3*(x^4+5)^(3/2)","A"
10,1,34,33,0.008000," ","int(x*(3*x^2+2)*(x^4+5)^(1/2),x)","\frac{\sqrt{x^{4}+5}\, x^{2}}{2}+\frac{5 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{2}+\frac{\left(x^{4}+5\right)^{\frac{3}{2}}}{2}"," ",0,"1/2*(x^4+5)^(3/2)+5/2*arcsinh(1/5*5^(1/2)*x^2)+1/2*(x^4+5)^(1/2)*x^2","A"
11,1,49,46,0.016000," ","int((3*x^2+2)*(x^4+5)^(1/2)/x,x)","\frac{3 \sqrt{x^{4}+5}\, x^{2}}{4}+\frac{15 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{4}-\sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{x^{4}+5}}\right)+\sqrt{x^{4}+5}"," ",0,"3/4*(x^4+5)^(1/2)*x^2+15/4*arcsinh(1/5*5^(1/2)*x^2)+(x^4+5)^(1/2)-5^(1/2)*arctanh(5^(1/2)/(x^4+5)^(1/2))","A"
12,1,61,47,0.013000," ","int((3*x^2+2)*(x^4+5)^(1/2)/x^3,x)","\frac{\sqrt{x^{4}+5}\, x^{2}}{5}+\arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)-\frac{3 \sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{x^{4}+5}}\right)}{2}-\frac{\left(x^{4}+5\right)^{\frac{3}{2}}}{5 x^{2}}+\frac{3 \sqrt{x^{4}+5}}{2}"," ",0,"3/2*(x^4+5)^(1/2)-3/2*5^(1/2)*arctanh(5^(1/2)/(x^4+5)^(1/2))-1/5/x^2*(x^4+5)^(3/2)+1/5*(x^4+5)^(1/2)*x^2+arcsinh(1/5*5^(1/2)*x^2)","A"
13,1,75,49,0.016000," ","int((3*x^2+2)*(x^4+5)^(1/2)/x^5,x)","\frac{3 \sqrt{x^{4}+5}\, x^{2}}{10}+\frac{3 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{2}-\frac{\sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{x^{4}+5}}\right)}{10}-\frac{3 \left(x^{4}+5\right)^{\frac{3}{2}}}{10 x^{2}}-\frac{\left(x^{4}+5\right)^{\frac{3}{2}}}{10 x^{4}}+\frac{\sqrt{x^{4}+5}}{10}"," ",0,"-1/10/x^4*(x^4+5)^(3/2)+1/10*(x^4+5)^(1/2)-1/10*5^(1/2)*arctanh(5^(1/2)/(x^4+5)^(1/2))-3/10*(x^4+5)^(3/2)/x^2+3/10*(x^4+5)^(1/2)*x^2+3/2*arcsinh(1/5*5^(1/2)*x^2)","A"
14,1,52,43,0.013000," ","int((3*x^2+2)*(x^4+5)^(1/2)/x^7,x)","-\frac{3 \sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{x^{4}+5}}\right)}{20}-\frac{3 \left(x^{4}+5\right)^{\frac{3}{2}}}{20 x^{4}}-\frac{\left(x^{4}+5\right)^{\frac{3}{2}}}{15 x^{6}}+\frac{3 \sqrt{x^{4}+5}}{20}"," ",0,"-1/15*(x^4+5)^(3/2)/x^6-3/20*(x^4+5)^(3/2)/x^4+3/20*(x^4+5)^(1/2)-3/20*5^(1/2)*arctanh(5^(1/2)/(x^4+5)^(1/2))","A"
15,1,192,224,0.090000," ","int(x^4*(3*x^2+2)*(x^4+5)^(1/2),x)","\frac{\sqrt{x^{4}+5}\, x^{7}}{3}+\frac{2 \sqrt{x^{4}+5}\, x^{5}}{7}+\frac{2 \sqrt{x^{4}+5}\, x^{3}}{3}+\frac{20 \sqrt{x^{4}+5}\, x}{21}-\frac{4 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{21 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}-\frac{2 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{\sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"1/3*x^7*(x^4+5)^(1/2)+2/3*x^3*(x^4+5)^(1/2)-2*I/(I*5^(1/2))^(1/2)*(25-5*I*5^(1/2)*x^2)^(1/2)*(25+5*I*5^(1/2)*x^2)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*x*5^(1/2)*(I*5^(1/2))^(1/2),I)-EllipticE(1/5*x*5^(1/2)*(I*5^(1/2))^(1/2),I))+2/7*x^5*(x^4+5)^(1/2)+20/21*x*(x^4+5)^(1/2)-4/21*5^(1/2)/(I*5^(1/2))^(1/2)*(25-5*I*5^(1/2)*x^2)^(1/2)*(25+5*I*5^(1/2)*x^2)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*x*5^(1/2)*(I*5^(1/2))^(1/2),I)","C"
16,1,180,212,0.020000," ","int(x^2*(3*x^2+2)*(x^4+5)^(1/2),x)","\frac{3 \sqrt{x^{4}+5}\, x^{5}}{7}+\frac{2 \sqrt{x^{4}+5}\, x^{3}}{5}+\frac{10 \sqrt{x^{4}+5}\, x}{7}-\frac{2 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{7 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}+\frac{4 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{5 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"3/7*(x^4+5)^(1/2)*x^5+10/7*(x^4+5)^(1/2)*x-2/7*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)+2/5*(x^4+5)^(1/2)*x^3+4/5*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))","C"
17,1,168,200,0.012000," ","int((3*x^2+2)*(x^4+5)^(1/2),x)","\frac{3 \sqrt{x^{4}+5}\, x^{3}}{5}+\frac{2 \sqrt{x^{4}+5}\, x}{3}+\frac{4 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{15 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}+\frac{6 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{5 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"3/5*(x^4+5)^(1/2)*x^3+6/5*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))+2/3*(x^4+5)^(1/2)*x+4/15*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)","C"
18,1,167,199,0.018000," ","int((3*x^2+2)*(x^4+5)^(1/2)/x^2,x)","\sqrt{x^{4}+5}\, x +\frac{2 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{5 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}-\frac{2 \sqrt{x^{4}+5}}{x}+\frac{4 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{5 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"(x^4+5)^(1/2)*x+2/5*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-2*(x^4+5)^(1/2)/x+4/5*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))","C"
19,1,170,214,0.017000," ","int((3*x^2+2)*(x^4+5)^(1/2)/x^4,x)","\frac{4 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{75 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}-\frac{3 \sqrt{x^{4}+5}}{x}-\frac{2 \sqrt{x^{4}+5}}{3 x^{3}}+\frac{6 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{5 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"-2/3*(x^4+5)^(1/2)/x^3+4/75*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-3*(x^4+5)^(1/2)/x+6/5*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))","C"
20,1,73,64,0.025000," ","int(x^5*(3*x^2+2)*(x^4+5)^(3/2),x)","\frac{\sqrt{x^{4}+5}\, x^{10}}{6}+\frac{35 \sqrt{x^{4}+5}\, x^{6}}{24}+\frac{25 \sqrt{x^{4}+5}\, x^{2}}{16}-\frac{125 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{16}+\frac{3 \sqrt{x^{4}+5}\, \left(x^{4}-2\right) \left(x^{8}+10 x^{4}+25\right)}{14}"," ",0,"3/14*(x^4+5)^(1/2)*(x^4-2)*(x^8+10*x^4+25)+1/6*x^10*(x^4+5)^(1/2)+35/24*x^6*(x^4+5)^(1/2)+25/16*(x^4+5)^(1/2)*x^2-125/16*arcsinh(1/5*5^(1/2)*x^2)","A"
21,1,58,52,0.009000," ","int(x^3*(3*x^2+2)*(x^4+5)^(3/2),x)","\frac{\sqrt{x^{4}+5}\, x^{10}}{4}+\frac{35 \sqrt{x^{4}+5}\, x^{6}}{16}+\frac{75 \sqrt{x^{4}+5}\, x^{2}}{32}-\frac{375 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{32}+\frac{\left(x^{4}+5\right)^{\frac{5}{2}}}{5}"," ",0,"1/4*(x^4+5)^(1/2)*x^10+35/16*(x^4+5)^(1/2)*x^6+75/32*(x^4+5)^(1/2)*x^2-375/32*arcsinh(1/5*5^(1/2)*x^2)+1/5*(x^4+5)^(5/2)","A"
22,1,46,45,0.014000," ","int(x*(3*x^2+2)*(x^4+5)^(3/2),x)","\frac{\sqrt{x^{4}+5}\, x^{6}}{4}+\frac{25 \sqrt{x^{4}+5}\, x^{2}}{8}+\frac{75 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{8}+\frac{3 \left(x^{4}+5\right)^{\frac{5}{2}}}{10}"," ",0,"3/10*(x^4+5)^(5/2)+1/4*(x^4+5)^(1/2)*x^6+25/8*(x^4+5)^(1/2)*x^2+75/8*arcsinh(1/5*5^(1/2)*x^2)","A"
23,1,75,62,0.020000," ","int((3*x^2+2)*(x^4+5)^(3/2)/x,x)","\frac{3 \sqrt{x^{4}+5}\, x^{6}}{8}+\frac{\sqrt{x^{4}+5}\, x^{4}}{3}+\frac{75 \sqrt{x^{4}+5}\, x^{2}}{16}+\frac{225 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{16}-5 \sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{x^{4}+5}}\right)+\frac{20 \sqrt{x^{4}+5}}{3}"," ",0,"3/8*(x^4+5)^(1/2)*x^6+75/16*(x^4+5)^(1/2)*x^2+225/16*arcsinh(1/5*5^(1/2)*x^2)+1/3*x^4*(x^4+5)^(1/2)+20/3*(x^4+5)^(1/2)-5*5^(1/2)*arctanh(5^(1/2)/(x^4+5)^(1/2))","A"
24,1,75,63,0.016000," ","int((3*x^2+2)*(x^4+5)^(3/2)/x^3,x)","\frac{\sqrt{x^{4}+5}\, x^{4}}{2}+\frac{\sqrt{x^{4}+5}\, x^{2}}{2}+\frac{15 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{2}-\frac{15 \sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{x^{4}+5}}\right)}{2}-\frac{5 \sqrt{x^{4}+5}}{x^{2}}+10 \sqrt{x^{4}+5}"," ",0,"1/2*(x^4+5)^(1/2)*x^4+10*(x^4+5)^(1/2)-15/2*5^(1/2)*arctanh(5^(1/2)/(x^4+5)^(1/2))+1/2*(x^4+5)^(1/2)*x^2+15/2*arcsinh(1/5*5^(1/2)*x^2)-5*(x^4+5)^(1/2)/x^2","A"
25,1,73,68,0.020000," ","int((3*x^2+2)*(x^4+5)^(3/2)/x^5,x)","\frac{3 \sqrt{x^{4}+5}\, x^{2}}{4}+\frac{45 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{4}-\frac{3 \sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{x^{4}+5}}\right)}{2}-\frac{15 \sqrt{x^{4}+5}}{2 x^{2}}-\frac{5 \sqrt{x^{4}+5}}{2 x^{4}}+\sqrt{x^{4}+5}"," ",0,"(x^4+5)^(1/2)-3/2*5^(1/2)*arctanh(5^(1/2)/(x^4+5)^(1/2))-5/2*(x^4+5)^(1/2)/x^4+3/4*(x^4+5)^(1/2)*x^2+45/4*arcsinh(1/5*5^(1/2)*x^2)-15/2*(x^4+5)^(1/2)/x^2","A"
26,1,73,66,0.023000," ","int((3*x^2+2)*(x^4+5)^(3/2)/x^7,x)","\arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)-\frac{9 \sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{x^{4}+5}}\right)}{4}-\frac{4 \sqrt{x^{4}+5}}{3 x^{2}}-\frac{15 \sqrt{x^{4}+5}}{4 x^{4}}-\frac{5 \sqrt{x^{4}+5}}{3 x^{6}}+\frac{3 \sqrt{x^{4}+5}}{2}"," ",0,"3/2*(x^4+5)^(1/2)-9/4*5^(1/2)*arctanh(5^(1/2)/(x^4+5)^(1/2))-15/4*(x^4+5)^(1/2)/x^4+arcsinh(1/5*5^(1/2)*x^2)-4/3*(x^4+5)^(1/2)/x^2-5/3*(x^4+5)^(1/2)/x^6","A"
27,1,216,243,0.020000," ","int(x^4*(3*x^2+2)*(x^4+5)^(3/2),x)","\frac{3 \sqrt{x^{4}+5}\, x^{11}}{13}+\frac{2 \sqrt{x^{4}+5}\, x^{9}}{11}+\frac{25 \sqrt{x^{4}+5}\, x^{7}}{13}+\frac{130 \sqrt{x^{4}+5}\, x^{5}}{77}+\frac{20 \sqrt{x^{4}+5}\, x^{3}}{13}+\frac{200 \sqrt{x^{4}+5}\, x}{77}-\frac{40 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{77 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}-\frac{60 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{13 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"3/13*x^11*(x^4+5)^(1/2)+25/13*(x^4+5)^(1/2)*x^7+20/13*(x^4+5)^(1/2)*x^3-60/13*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))+2/11*x^9*(x^4+5)^(1/2)+130/77*(x^4+5)^(1/2)*x^5+200/77*(x^4+5)^(1/2)*x-40/77*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)","C"
28,1,204,231,0.013000," ","int(x^2*(3*x^2+2)*(x^4+5)^(3/2),x)","\frac{3 \sqrt{x^{4}+5}\, x^{9}}{11}+\frac{2 \sqrt{x^{4}+5}\, x^{7}}{9}+\frac{195 \sqrt{x^{4}+5}\, x^{5}}{77}+\frac{22 \sqrt{x^{4}+5}\, x^{3}}{9}+\frac{300 \sqrt{x^{4}+5}\, x}{77}-\frac{60 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{77 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}+\frac{8 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{3 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"3/11*(x^4+5)^(1/2)*x^9+195/77*(x^4+5)^(1/2)*x^5+300/77*(x^4+5)^(1/2)*x-60/77*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)+2/9*(x^4+5)^(1/2)*x^7+22/9*(x^4+5)^(1/2)*x^3+8/3*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))","C"
29,1,192,217,0.011000," ","int((3*x^2+2)*(x^4+5)^(3/2),x)","\frac{\sqrt{x^{4}+5}\, x^{7}}{3}+\frac{2 \sqrt{x^{4}+5}\, x^{5}}{7}+\frac{11 \sqrt{x^{4}+5}\, x^{3}}{3}+\frac{30 \sqrt{x^{4}+5}\, x}{7}+\frac{8 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{7 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}+\frac{4 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{\sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"1/3*(x^4+5)^(1/2)*x^7+11/3*(x^4+5)^(1/2)*x^3+4*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))+2/7*(x^4+5)^(1/2)*x^5+30/7*(x^4+5)^(1/2)*x+8/7*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)","C"
30,1,192,219,0.018000," ","int((3*x^2+2)*(x^4+5)^(3/2)/x^2,x)","\frac{3 \sqrt{x^{4}+5}\, x^{5}}{7}+\frac{2 \sqrt{x^{4}+5}\, x^{3}}{5}+\frac{45 \sqrt{x^{4}+5}\, x}{7}+\frac{12 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{7 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}-\frac{10 \sqrt{x^{4}+5}}{x}+\frac{24 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{5 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"3/7*(x^4+5)^(1/2)*x^5+45/7*(x^4+5)^(1/2)*x+12/7*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-10*(x^4+5)^(1/2)/x+2/5*(x^4+5)^(1/2)*x^3+24/5*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))","C"
31,1,192,221,0.017000," ","int((3*x^2+2)*(x^4+5)^(3/2)/x^4,x)","\frac{3 \sqrt{x^{4}+5}\, x^{3}}{5}+\frac{2 \sqrt{x^{4}+5}\, x}{3}+\frac{8 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{15 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}-\frac{15 \sqrt{x^{4}+5}}{x}-\frac{10 \sqrt{x^{4}+5}}{3 x^{3}}+\frac{36 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{5 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"-15*(x^4+5)^(1/2)/x+3/5*(x^4+5)^(1/2)*x^3+36/5*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))-10/3*(x^4+5)^(1/2)/x^3+2/3*(x^4+5)^(1/2)*x+8/15*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)","C"
32,1,51,52,0.018000," ","int(x^7*(3*x^2+2)/(x^4+5)^(1/2),x)","\frac{3 \sqrt{x^{4}+5}\, x^{6}}{8}-\frac{45 \sqrt{x^{4}+5}\, x^{2}}{16}+\frac{225 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{16}+\frac{\sqrt{x^{4}+5}\, \left(x^{4}-10\right)}{3}"," ",0,"3/8*(x^4+5)^(1/2)*x^6-45/16*(x^4+5)^(1/2)*x^2+225/16*arcsinh(1/5*5^(1/2)*x^2)+1/3*(x^4+5)^(1/2)*(x^4-10)","A"
33,1,39,40,0.012000," ","int(x^5*(3*x^2+2)/(x^4+5)^(1/2),x)","\frac{\sqrt{x^{4}+5}\, x^{2}}{2}-\frac{5 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{2}+\frac{\sqrt{x^{4}+5}\, \left(x^{4}-10\right)}{2}"," ",0,"1/2*(x^4+5)^(1/2)*(x^4-10)+1/2*(x^4+5)^(1/2)*x^2-5/2*arcsinh(1/5*5^(1/2)*x^2)","A"
34,1,32,28,0.007000," ","int(x^3*(3*x^2+2)/(x^4+5)^(1/2),x)","\frac{3 \sqrt{x^{4}+5}\, x^{2}}{4}-\frac{15 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{4}+\sqrt{x^{4}+5}"," ",0,"3/4*(x^4+5)^(1/2)*x^2-15/4*arcsinh(1/5*5^(1/2)*x^2)+(x^4+5)^(1/2)","A"
35,1,20,19,0.010000," ","int(x*(3*x^2+2)/(x^4+5)^(1/2),x)","\arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)+\frac{3 \sqrt{x^{4}+5}}{2}"," ",0,"arcsinh(1/5*5^(1/2)*x^2)+3/2*(x^4+5)^(1/2)","A"
36,1,30,30,0.013000," ","int((3*x^2+2)/x/(x^4+5)^(1/2),x)","\frac{3 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{2}-\frac{\sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{x^{4}+5}}\right)}{5}"," ",0,"3/2*arcsinh(1/5*5^(1/2)*x^2)-1/5*5^(1/2)*arctanh(5^(1/2)/(x^4+5)^(1/2))","A"
37,1,31,31,0.014000," ","int((3*x^2+2)/x^3/(x^4+5)^(1/2),x)","-\frac{3 \sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{x^{4}+5}}\right)}{10}-\frac{\sqrt{x^{4}+5}}{5 x^{2}}"," ",0,"-3/10*5^(1/2)*arctanh(5^(1/2)/(x^4+5)^(1/2))-1/5*(x^4+5)^(1/2)/x^2","A"
38,1,43,43,0.019000," ","int((3*x^2+2)/x^5/(x^4+5)^(1/2),x)","\frac{\sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{x^{4}+5}}\right)}{50}-\frac{3 \sqrt{x^{4}+5}}{10 x^{2}}-\frac{\sqrt{x^{4}+5}}{10 x^{4}}"," ",0,"-1/10*(x^4+5)^(1/2)/x^4+1/50*5^(1/2)*arctanh(5^(1/2)/(x^4+5)^(1/2))-3/10*(x^4+5)^(1/2)/x^2","A"
39,1,168,205,0.023000," ","int(x^4*(3*x^2+2)/(x^4+5)^(1/2),x)","\frac{3 \sqrt{x^{4}+5}\, x^{3}}{5}+\frac{2 \sqrt{x^{4}+5}\, x}{3}-\frac{2 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{15 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}-\frac{9 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{5 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"3/5*(x^4+5)^(1/2)*x^3-9/5*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))+2/3*(x^4+5)^(1/2)*x-2/15*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)","C"
40,1,155,192,0.013000," ","int(x^2*(3*x^2+2)/(x^4+5)^(1/2),x)","\sqrt{x^{4}+5}\, x -\frac{\sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{5 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}+\frac{2 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{5 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"(x^4+5)^(1/2)*x-1/5*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)+2/5*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))","C"
41,1,146,183,0.010000," ","int((3*x^2+2)/(x^4+5)^(1/2),x)","\frac{2 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{25 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}+\frac{3 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{5 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"3/5*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))+2/25*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)","C"
42,1,158,195,0.019000," ","int((3*x^2+2)/x^2/(x^4+5)^(1/2),x)","\frac{3 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{25 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}-\frac{2 \sqrt{x^{4}+5}}{5 x}+\frac{2 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{25 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"3/25*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-2/5*(x^4+5)^(1/2)/x+2/25*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))","C"
43,1,170,207,0.024000," ","int((3*x^2+2)/x^4/(x^4+5)^(1/2),x)","-\frac{2 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{375 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}-\frac{3 \sqrt{x^{4}+5}}{5 x}-\frac{2 \sqrt{x^{4}+5}}{15 x^{3}}+\frac{3 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{25 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"-3/5*(x^4+5)^(1/2)/x+3/25*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))-2/15*(x^4+5)^(1/2)/x^3-2/375*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)","C"
44,1,50,47,0.021000," ","int(x^7*(3*x^2+2)/(x^4+5)^(3/2),x)","\frac{3 x^{6}}{4 \sqrt{x^{4}+5}}+\frac{45 x^{2}}{4 \sqrt{x^{4}+5}}-\frac{45 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{4}+\frac{x^{4}+10}{\sqrt{x^{4}+5}}"," ",0,"3/4*x^6/(x^4+5)^(1/2)+45/4*x^2/(x^4+5)^(1/2)-45/4*arcsinh(1/5*5^(1/2)*x^2)+1/(x^4+5)^(1/2)*(x^4+10)","A"
45,1,37,38,0.014000," ","int(x^5*(3*x^2+2)/(x^4+5)^(3/2),x)","-\frac{x^{2}}{\sqrt{x^{4}+5}}+\arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)+\frac{\frac{3 x^{4}}{2}+15}{\sqrt{x^{4}+5}}"," ",0,"3/2/(x^4+5)^(1/2)*(x^4+10)-1/(x^4+5)^(1/2)*x^2+arcsinh(1/5*5^(1/2)*x^2)","A"
46,1,34,28,0.007000," ","int(x^3*(3*x^2+2)/(x^4+5)^(3/2),x)","-\frac{3 x^{2}}{2 \sqrt{x^{4}+5}}+\frac{3 \arcsinh \left(\frac{\sqrt{5}\, x^{2}}{5}\right)}{2}-\frac{1}{\sqrt{x^{4}+5}}"," ",0,"-3/2/(x^4+5)^(1/2)*x^2+3/2*arcsinh(1/5*5^(1/2)*x^2)-1/(x^4+5)^(1/2)","A"
47,1,17,16,0.003000," ","int(x*(3*x^2+2)/(x^4+5)^(3/2),x)","\frac{2 x^{2}-15}{10 \sqrt{x^{4}+5}}"," ",0,"1/10*(2*x^2-15)/(x^4+5)^(1/2)","A"
48,1,40,35,0.020000," ","int((3*x^2+2)/x/(x^4+5)^(3/2),x)","\frac{3 x^{2}}{10 \sqrt{x^{4}+5}}-\frac{\sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{x^{4}+5}}\right)}{25}+\frac{1}{5 \sqrt{x^{4}+5}}"," ",0,"3/10/(x^4+5)^(1/2)*x^2+1/5/(x^4+5)^(1/2)-1/25*5^(1/2)*arctanh(5^(1/2)/(x^4+5)^(1/2))","A"
49,1,47,50,0.014000," ","int((3*x^2+2)/x^3/(x^4+5)^(3/2),x)","-\frac{3 \sqrt{5}\, \arctanh \left(\frac{\sqrt{5}}{\sqrt{x^{4}+5}}\right)}{50}-\frac{2 x^{4}+5}{25 \sqrt{x^{4}+5}\, x^{2}}+\frac{3}{10 \sqrt{x^{4}+5}}"," ",0,"3/10/(x^4+5)^(1/2)-3/50*5^(1/2)*arctanh(5^(1/2)/(x^4+5)^(1/2))-1/25/x^2*(2*x^4+5)/(x^4+5)^(1/2)","A"
50,1,168,212,0.025000," ","int(x^4*(3*x^2+2)/(x^4+5)^(3/2),x)","-\frac{3 x^{3}}{2 \sqrt{x^{4}+5}}-\frac{x}{\sqrt{x^{4}+5}}+\frac{\sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{25 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}+\frac{9 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{10 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"-3/2*x^3/(x^4+5)^(1/2)+9/10*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))-x/(x^4+5)^(1/2)+1/25*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)","C"
51,1,168,200,0.017000," ","int(x^2*(3*x^2+2)/(x^4+5)^(3/2),x)","\frac{x^{3}}{5 \sqrt{x^{4}+5}}-\frac{3 x}{2 \sqrt{x^{4}+5}}+\frac{3 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{50 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}-\frac{i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{25 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"-3/2/(x^4+5)^(1/2)*x+3/50*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)+1/5/(x^4+5)^(1/2)*x^3-1/25*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))","C"
52,1,168,200,0.014000," ","int((3*x^2+2)/(x^4+5)^(3/2),x)","\frac{3 x^{3}}{10 \sqrt{x^{4}+5}}+\frac{x}{5 \sqrt{x^{4}+5}}+\frac{\sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{125 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}-\frac{3 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{50 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"3/10/(x^4+5)^(1/2)*x^3-3/50*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))+1/5/(x^4+5)^(1/2)*x+1/125*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)","C"
53,1,180,212,0.021000," ","int((3*x^2+2)/x^2/(x^4+5)^(3/2),x)","-\frac{x^{3}}{25 \sqrt{x^{4}+5}}+\frac{3 x}{10 \sqrt{x^{4}+5}}+\frac{3 \sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{250 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}-\frac{2 \sqrt{x^{4}+5}}{25 x}+\frac{3 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{125 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"3/10/(x^4+5)^(1/2)*x+3/250*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-2/25*(x^4+5)^(1/2)/x-1/25/(x^4+5)^(1/2)*x^3+3/125*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))","C"
54,1,192,226,0.020000," ","int((3*x^2+2)/x^4/(x^4+5)^(3/2),x)","-\frac{3 x^{3}}{50 \sqrt{x^{4}+5}}-\frac{x}{25 \sqrt{x^{4}+5}}-\frac{\sqrt{5}\, \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)}{375 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}-\frac{3 \sqrt{x^{4}+5}}{25 x}-\frac{2 \sqrt{x^{4}+5}}{75 x^{3}}+\frac{9 i \sqrt{-5 i \sqrt{5}\, x^{2}+25}\, \sqrt{5 i \sqrt{5}\, x^{2}+25}\, \left(-\EllipticE \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)+\EllipticF \left(\frac{\sqrt{5}\, \sqrt{i \sqrt{5}}\, x}{5}, i\right)\right)}{250 \sqrt{i \sqrt{5}}\, \sqrt{x^{4}+5}}"," ",0,"-3/25*(x^4+5)^(1/2)/x-3/50/(x^4+5)^(1/2)*x^3+9/250*I/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*(EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)-EllipticE(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I))-2/75*(x^4+5)^(1/2)/x^3-1/25/(x^4+5)^(1/2)*x-1/375*5^(1/2)/(I*5^(1/2))^(1/2)*(-5*I*5^(1/2)*x^2+25)^(1/2)*(5*I*5^(1/2)*x^2+25)^(1/2)/(x^4+5)^(1/2)*EllipticF(1/5*5^(1/2)*(I*5^(1/2))^(1/2)*x,I)","C"
55,1,2295,269,0.027000," ","int((f*x)^m*(e*x^2+d)*(x^4+2*x^2+1)^5,x)","\frac{\left(e \,m^{11} x^{22}+121 e \,m^{10} x^{22}+d \,m^{11} x^{20}+10 e \,m^{11} x^{20}+6435 e \,m^{9} x^{22}+123 d \,m^{10} x^{20}+1230 e \,m^{10} x^{20}+197835 e \,m^{8} x^{22}+10 d \,m^{11} x^{18}+6635 d \,m^{9} x^{20}+45 e \,m^{11} x^{18}+66350 e \,m^{9} x^{20}+3889578 e \,m^{7} x^{22}+1250 d \,m^{10} x^{18}+206505 d \,m^{8} x^{20}+5625 e \,m^{10} x^{18}+2065050 e \,m^{8} x^{20}+51069018 e \,m^{6} x^{22}+45 d \,m^{11} x^{16}+68430 d \,m^{9} x^{18}+4103178 d \,m^{7} x^{20}+120 e \,m^{11} x^{16}+307935 e \,m^{9} x^{18}+41031780 e \,m^{7} x^{20}+453714470 e \,m^{5} x^{22}+5715 d \,m^{10} x^{16}+2158230 d \,m^{8} x^{18}+54362574 d \,m^{6} x^{20}+15240 e \,m^{10} x^{16}+9712035 e \,m^{8} x^{18}+543625740 e \,m^{6} x^{20}+2702025590 e \,m^{4} x^{22}+120 d \,m^{11} x^{14}+317655 d \,m^{9} x^{16}+43391460 d \,m^{7} x^{18}+486687830 d \,m^{5} x^{20}+210 e \,m^{11} x^{14}+847080 e \,m^{9} x^{16}+195261570 e \,m^{7} x^{18}+4866878300 e \,m^{5} x^{20}+10431670821 e \,m^{3} x^{22}+15480 d \,m^{10} x^{14}+10162665 d \,m^{8} x^{16}+580855380 d \,m^{6} x^{18}+2917013970 d \,m^{4} x^{20}+27090 e \,m^{10} x^{14}+27100440 e \,m^{8} x^{16}+2613849210 e \,m^{6} x^{18}+29170139700 e \,m^{4} x^{20}+24372200061 e \,m^{2} x^{22}+210 d \,m^{11} x^{12}+873960 d \,m^{9} x^{14}+207024930 d \,m^{7} x^{16}+5246766620 d \,m^{5} x^{18}+11320966021 d \,m^{3} x^{20}+252 e \,m^{11} x^{12}+1529430 e \,m^{9} x^{14}+552066480 e \,m^{7} x^{16}+23610449790 e \,m^{5} x^{18}+113209660210 e \,m^{3} x^{20}+29985521895 e m \,x^{22}+27510 d \,m^{10} x^{12}+28391400 d \,m^{8} x^{14}+2804395230 d \,m^{6} x^{16}+31686018220 d \,m^{4} x^{18}+26560342503 d \,m^{2} x^{20}+33012 e \,m^{10} x^{12}+49684950 e \,m^{8} x^{14}+7478387280 e \,m^{6} x^{16}+142587081990 e \,m^{4} x^{18}+265603425030 e \,m^{2} x^{20}+13749310575 e \,x^{22}+252 d \,m^{11} x^{10}+1578150 d \,m^{9} x^{12}+586902960 d \,m^{7} x^{14}+25598865870 d \,m^{5} x^{16}+123748247730 d \,m^{3} x^{18}+32778930735 d m \,x^{20}+210 e \,m^{11} x^{10}+1893780 e \,m^{9} x^{12}+1027080180 e \,m^{7} x^{14}+68263642320 e \,m^{5} x^{16}+556867114785 e \,m^{3} x^{18}+327789307350 e m \,x^{20}+33516 d \,m^{10} x^{10}+52110450 d \,m^{8} x^{12}+8059973040 d \,m^{6} x^{14}+156004908210 d \,m^{4} x^{16}+291789582570 d \,m^{2} x^{18}+15058768725 d \,x^{20}+27930 e \,m^{10} x^{10}+62532540 e \,m^{8} x^{12}+14104952820 e \,m^{6} x^{14}+416013088560 e \,m^{4} x^{16}+1313053121565 e \,m^{2} x^{18}+150587687250 e \,x^{20}+210 d \,m^{11} x^{8}+1954260 d \,m^{9} x^{10}+1094918580 d \,m^{7} x^{12}+74496630480 d \,m^{5} x^{14}+613938233025 d \,m^{3} x^{16}+361459164150 d m \,x^{18}+120 e \,m^{11} x^{8}+1628550 e \,m^{9} x^{10}+1313902296 e \,m^{7} x^{12}+130369103340 e \,m^{5} x^{14}+1637168621400 e \,m^{3} x^{16}+1626566238675 e m \,x^{18}+28350 d \,m^{10} x^{8}+65654820 d \,m^{8} x^{10}+15277213980 d \,m^{6} x^{12}+459045550800 d \,m^{4} x^{14}+1456578341055 d \,m^{2} x^{16}+166439022750 d \,x^{18}+16200 e \,m^{10} x^{8}+54712350 e \,m^{8} x^{10}+18332656776 e \,m^{6} x^{12}+803329713900 e \,m^{4} x^{14}+3884208909480 e \,m^{2} x^{16}+748975602375 e \,x^{18}+120 d \,m^{11} x^{6}+1680630 d \,m^{9} x^{8}+1404622296 d \,m^{7} x^{10}+143339613900 d \,m^{5} x^{12}+1823707864920 d \,m^{3} x^{14}+1812743750475 d m \,x^{16}+45 e \,m^{11} x^{6}+960360 e \,m^{9} x^{8}+1170518580 e \,m^{7} x^{10}+172007536680 e \,m^{5} x^{12}+3191488763610 e \,m^{3} x^{14}+4833983334600 e m \,x^{16}+16440 d \,m^{10} x^{6}+57500730 d \,m^{8} x^{8}+19962541368 d \,m^{6} x^{10}+895451283300 d \,m^{4} x^{12}+4360457499480 d \,m^{2} x^{14}+837090379125 d \,x^{16}+6165 e \,m^{10} x^{6}+32857560 e \,m^{8} x^{8}+16635451140 e \,m^{6} x^{10}+1074541539960 e \,m^{4} x^{12}+7630800624090 e \,m^{2} x^{14}+2232241011000 e \,x^{16}+45 d \,m^{11} x^{4}+991080 d \,m^{9} x^{6}+1254847860 d \,m^{7} x^{8}+190744119720 d \,m^{5} x^{10}+3600567789210 d \,m^{3} x^{12}+5458672303560 d m \,x^{14}+10 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x^{4}+8511631481880 d \,m^{2} x^{6}+7378796675250 d \,x^{8}+118085058 e \,m^{6} x^{2}+76437245300 e \,m^{4} x^{4}+3191861805705 e \,m^{2} x^{6}+4216455243000 e \,x^{8}+8103018 d \,m^{7}+12740467100 d \,m^{5} x^{2}+1546183653345 d \,m^{3} x^{4}+11284114422600 d m \,x^{6}+1274046710 e \,m^{5} x^{2}+343596367410 e \,m^{3} x^{4}+4231542908475 e m \,x^{6}+132426294 d \,m^{6}+93153182700 d \,m^{4} x^{2}+4162610035755 d \,m^{2} x^{4}+5421156741000 d \,x^{6}+9315318270 e \,m^{4} x^{2}+925024452390 e \,m^{2} x^{4}+2032933777875 e \,x^{6}+1495875590 d \,m^{5}+446323045810 d \,m^{3} x^{2}+5761525369635 d m \,x^{4}+44632304581 e \,m^{3} x^{2}+1280338971030 e m \,x^{4}+11641582810 d \,m^{4}+1304037152010 d \,m^{2} x^{2}+2846107289025 d \,x^{4}+130403715201 e \,m^{2} x^{2}+632468286450 e \,x^{4}+60936676581 d \,m^{3}+1993349776950 d m \,x^{2}+199334977695 e m \,x^{2}+203363952363 d \,m^{2}+1054113810750 d \,x^{2}+105411381075 e \,x^{2}+387182170935 d m +316234143225 d \right) x \left(f x \right)^{m}}{\left(m +1\right) \left(m +3\right) \left(m +5\right) \left(m +7\right) \left(m +9\right) \left(m +11\right) \left(m +13\right) \left(m +15\right) \left(m +17\right) \left(m +19\right) \left(m +21\right) \left(m +23\right)}"," 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*x^4+2032933777875*e*x^6+1495875590*d*m^5+446323045810*d*m^3*x^2+5761525369635*d*m*x^4+44632304581*e*m^3*x^2+1280338971030*e*m*x^4+11641582810*d*m^4+1304037152010*d*m^2*x^2+2846107289025*d*x^4+130403715201*e*m^2*x^2+632468286450*e*x^4+60936676581*d*m^3+1993349776950*d*m*x^2+199334977695*e*m*x^2+203363952363*d*m^2+1054113810750*d*x^2+105411381075*e*x^2+387182170935*d*m+316234143225*d)*x/(1+m)/(3+m)/(5+m)/(7+m)/(9+m)/(11+m)/(13+m)/(15+m)/(17+m)/(19+m)/(21+m)/(23+m)","B"
56,1,130,55,0.002000," ","int(x^5*(e*x^2+d)*(x^4+2*x^2+1)^5,x)","\frac{e \,x^{28}}{28}+\frac{\left(d +10 e \right) x^{26}}{26}+\frac{\left(10 d +45 e \right) x^{24}}{24}+\frac{\left(45 d +120 e \right) x^{22}}{22}+\frac{\left(120 d +210 e \right) x^{20}}{20}+\frac{\left(210 d +252 e \right) x^{18}}{18}+\frac{\left(252 d +210 e \right) x^{16}}{16}+\frac{\left(210 d +120 e \right) x^{14}}{14}+\frac{\left(120 d +45 e \right) x^{12}}{12}+\frac{\left(45 d +10 e \right) x^{10}}{10}+\frac{\left(10 d +e \right) x^{8}}{8}+\frac{d \,x^{6}}{6}"," ",0,"1/28*e*x^28+1/26*(d+10*e)*x^26+1/24*(10*d+45*e)*x^24+1/22*(45*d+120*e)*x^22+1/20*(120*d+210*e)*x^20+1/18*(210*d+252*e)*x^18+1/16*(252*d+210*e)*x^16+1/14*(210*d+120*e)*x^14+1/12*(120*d+45*e)*x^12+1/10*(45*d+10*e)*x^10+1/8*(10*d+e)*x^8+1/6*d*x^6","B"
57,1,130,129,0.000000," ","int(x^4*(e*x^2+d)*(x^4+2*x^2+1)^5,x)","\frac{e \,x^{27}}{27}+\frac{\left(d +10 e \right) x^{25}}{25}+\frac{\left(10 d +45 e \right) x^{23}}{23}+\frac{\left(45 d +120 e \right) x^{21}}{21}+\frac{\left(120 d +210 e \right) x^{19}}{19}+\frac{\left(210 d +252 e \right) x^{17}}{17}+\frac{\left(252 d +210 e \right) x^{15}}{15}+\frac{\left(210 d +120 e \right) x^{13}}{13}+\frac{\left(120 d +45 e \right) x^{11}}{11}+\frac{\left(45 d +10 e \right) x^{9}}{9}+\frac{\left(10 d +e \right) x^{7}}{7}+\frac{d \,x^{5}}{5}"," ",0,"1/27*e*x^27+1/25*(d+10*e)*x^25+1/23*(10*d+45*e)*x^23+1/21*(45*d+120*e)*x^21+1/19*(120*d+210*e)*x^19+1/17*(210*d+252*e)*x^17+1/15*(252*d+210*e)*x^15+1/13*(210*d+120*e)*x^13+1/11*(120*d+45*e)*x^11+1/9*(45*d+10*e)*x^9+1/7*(10*d+e)*x^7+1/5*d*x^5","A"
58,1,130,39,0.000000," ","int(x^3*(e*x^2+d)*(x^4+2*x^2+1)^5,x)","\frac{e \,x^{26}}{26}+\frac{\left(d +10 e \right) x^{24}}{24}+\frac{\left(10 d +45 e \right) x^{22}}{22}+\frac{\left(45 d +120 e \right) x^{20}}{20}+\frac{\left(120 d +210 e \right) x^{18}}{18}+\frac{\left(210 d +252 e \right) x^{16}}{16}+\frac{\left(252 d +210 e \right) x^{14}}{14}+\frac{\left(210 d +120 e \right) x^{12}}{12}+\frac{\left(120 d +45 e \right) x^{10}}{10}+\frac{\left(45 d +10 e \right) x^{8}}{8}+\frac{\left(10 d +e \right) x^{6}}{6}+\frac{d \,x^{4}}{4}"," ",0,"1/26*e*x^26+1/24*(d+10*e)*x^24+1/22*(10*d+45*e)*x^22+1/20*(45*d+120*e)*x^20+1/18*(120*d+210*e)*x^18+1/16*(210*d+252*e)*x^16+1/14*(252*d+210*e)*x^14+1/12*(210*d+120*e)*x^12+1/10*(120*d+45*e)*x^10+1/8*(45*d+10*e)*x^8+1/6*(10*d+e)*x^6+1/4*d*x^4","B"
59,1,130,129,0.002000," ","int(x^2*(e*x^2+d)*(x^4+2*x^2+1)^5,x)","\frac{e \,x^{25}}{25}+\frac{\left(d +10 e \right) x^{23}}{23}+\frac{\left(10 d +45 e \right) x^{21}}{21}+\frac{\left(45 d +120 e \right) x^{19}}{19}+\frac{\left(120 d +210 e \right) x^{17}}{17}+\frac{\left(210 d +252 e \right) x^{15}}{15}+\frac{\left(252 d +210 e \right) x^{13}}{13}+\frac{\left(210 d +120 e \right) x^{11}}{11}+\frac{\left(120 d +45 e \right) x^{9}}{9}+\frac{\left(45 d +10 e \right) x^{7}}{7}+\frac{\left(10 d +e \right) x^{5}}{5}+\frac{d \,x^{3}}{3}"," ",0,"1/25*e*x^25+1/23*(d+10*e)*x^23+1/21*(10*d+45*e)*x^21+1/19*(45*d+120*e)*x^19+1/17*(120*d+210*e)*x^17+1/15*(210*d+252*e)*x^15+1/13*(252*d+210*e)*x^13+1/11*(210*d+120*e)*x^11+1/9*(120*d+45*e)*x^9+1/7*(45*d+10*e)*x^7+1/5*(10*d+e)*x^5+1/3*d*x^3","A"
60,1,130,25,0.002000," ","int(x*(e*x^2+d)*(x^4+2*x^2+1)^5,x)","\frac{e \,x^{24}}{24}+\frac{\left(d +10 e \right) x^{22}}{22}+\frac{\left(10 d +45 e \right) x^{20}}{20}+\frac{\left(45 d +120 e \right) x^{18}}{18}+\frac{\left(120 d +210 e \right) x^{16}}{16}+\frac{\left(210 d +252 e \right) x^{14}}{14}+\frac{\left(252 d +210 e \right) x^{12}}{12}+\frac{\left(210 d +120 e \right) x^{10}}{10}+\frac{\left(120 d +45 e \right) x^{8}}{8}+\frac{\left(45 d +10 e \right) x^{6}}{6}+\frac{\left(10 d +e \right) x^{4}}{4}+\frac{d \,x^{2}}{2}"," ",0,"1/24*e*x^24+1/22*(d+10*e)*x^22+1/20*(10*d+45*e)*x^20+1/18*(45*d+120*e)*x^18+1/16*(120*d+210*e)*x^16+1/14*(210*d+252*e)*x^14+1/12*(252*d+210*e)*x^12+1/10*(210*d+120*e)*x^10+1/8*(120*d+45*e)*x^8+1/6*(45*d+10*e)*x^6+1/4*(10*d+e)*x^4+1/2*d*x^2","B"
61,1,127,125,0.001000," ","int((e*x^2+d)*(x^4+2*x^2+1)^5,x)","\frac{e \,x^{23}}{23}+\frac{\left(d +10 e \right) x^{21}}{21}+\frac{\left(10 d +45 e \right) x^{19}}{19}+\frac{\left(45 d +120 e \right) x^{17}}{17}+\frac{\left(120 d +210 e \right) x^{15}}{15}+\frac{\left(210 d +252 e \right) x^{13}}{13}+\frac{\left(252 d +210 e \right) x^{11}}{11}+\frac{\left(210 d +120 e \right) x^{9}}{9}+\frac{\left(120 d +45 e \right) x^{7}}{7}+\frac{\left(45 d +10 e \right) x^{5}}{5}+\frac{\left(10 d +e \right) x^{3}}{3}+d x"," ",0,"1/23*e*x^23+1/21*(d+10*e)*x^21+1/19*(10*d+45*e)*x^19+1/17*(45*d+120*e)*x^17+1/15*(120*d+210*e)*x^15+1/13*(210*d+252*e)*x^13+1/11*(252*d+210*e)*x^11+1/9*(210*d+120*e)*x^9+1/7*(120*d+45*e)*x^7+1/5*(45*d+10*e)*x^5+1/3*(10*d+e)*x^3+d*x","A"
62,1,132,75,0.003000," ","int((e*x^2+d)*(x^4+2*x^2+1)^5/x,x)","\frac{e \,x^{22}}{22}+\frac{d \,x^{20}}{20}+\frac{e \,x^{20}}{2}+\frac{5 d \,x^{18}}{9}+\frac{5 e \,x^{18}}{2}+\frac{45 d \,x^{16}}{16}+\frac{15 e \,x^{16}}{2}+\frac{60 d \,x^{14}}{7}+15 e \,x^{14}+\frac{35 d \,x^{12}}{2}+21 e \,x^{12}+\frac{126 d \,x^{10}}{5}+21 e \,x^{10}+\frac{105 d \,x^{8}}{4}+15 e \,x^{8}+20 d \,x^{6}+\frac{15 e \,x^{6}}{2}+\frac{45 d \,x^{4}}{4}+\frac{5 e \,x^{4}}{2}+5 d \,x^{2}+\frac{e \,x^{2}}{2}+d \ln \left(x \right)"," ",0,"1/22*e*x^22+1/20*d*x^20+1/2*e*x^20+5/9*d*x^18+5/2*e*x^18+45/16*d*x^16+15/2*x^16*e+60/7*d*x^14+15*e*x^14+35/2*d*x^12+21*e*x^12+126/5*d*x^10+21*e*x^10+105/4*d*x^8+15*e*x^8+20*d*x^6+15/2*e*x^6+45/4*d*x^4+5/2*e*x^4+5*d*x^2+1/2*e*x^2+d*ln(x)","A"
63,1,129,125,0.005000," ","int((e*x^2+d)*(x^4+2*x^2+1)^5/x^2,x)","\frac{e \,x^{21}}{21}+\frac{d \,x^{19}}{19}+\frac{10 e \,x^{19}}{19}+\frac{10 d \,x^{17}}{17}+\frac{45 e \,x^{17}}{17}+3 d \,x^{15}+8 e \,x^{15}+\frac{120 d \,x^{13}}{13}+\frac{210 e \,x^{13}}{13}+\frac{210 d \,x^{11}}{11}+\frac{252 e \,x^{11}}{11}+28 d \,x^{9}+\frac{70 e \,x^{9}}{3}+30 d \,x^{7}+\frac{120 e \,x^{7}}{7}+24 d \,x^{5}+9 e \,x^{5}+15 d \,x^{3}+\frac{10 e \,x^{3}}{3}+10 d x +e x -\frac{d}{x}"," ",0,"1/21*e*x^21+1/19*x^19*d+10/19*x^19*e+10/17*x^17*d+45/17*x^17*e+3*x^15*d+8*x^15*e+120/13*x^13*d+210/13*x^13*e+210/11*x^11*d+252/11*x^11*e+28*x^9*d+70/3*x^9*e+30*x^7*d+120/7*x^7*e+24*d*x^5+9*x^5*e+15*d*x^3+10/3*x^3*e+10*d*x+e*x-d/x","A"
64,1,131,127,0.007000," ","int((e*x^2+d)*(x^4+2*x^2+1)^5/x^3,x)","\frac{e \,x^{20}}{20}+\frac{d \,x^{18}}{18}+\frac{5 e \,x^{18}}{9}+\frac{5 d \,x^{16}}{8}+\frac{45 e \,x^{16}}{16}+\frac{45 d \,x^{14}}{14}+\frac{60 e \,x^{14}}{7}+10 d \,x^{12}+\frac{35 e \,x^{12}}{2}+21 d \,x^{10}+\frac{126 e \,x^{10}}{5}+\frac{63 d \,x^{8}}{2}+\frac{105 e \,x^{8}}{4}+35 d \,x^{6}+20 e \,x^{6}+30 d \,x^{4}+\frac{45 e \,x^{4}}{4}+\frac{45 d \,x^{2}}{2}+5 e \,x^{2}+10 d \ln \left(x \right)+e \ln \left(x \right)-\frac{d}{2 x^{2}}"," ",0,"1/20*e*x^20+1/18*d*x^18+5/9*e*x^18+5/8*d*x^16+45/16*e*x^16+45/14*d*x^14+60/7*e*x^14+10*d*x^12+35/2*e*x^12+21*d*x^10+126/5*e*x^10+63/2*d*x^8+105/4*e*x^8+35*d*x^6+20*e*x^6+30*d*x^4+45/4*e*x^4+45/2*d*x^2+5*e*x^2+10*d*ln(x)+ln(x)*e-1/2*d/x^2","A"
65,1,1121,203,0.013000," ","int((f*x)^m*(x^2+1)*(x^4+2*x^2+1)^5,x)","\frac{\left(m^{11} x^{22}+121 m^{10} x^{22}+11 m^{11} x^{20}+6435 m^{9} x^{22}+1353 m^{10} x^{20}+197835 m^{8} x^{22}+55 m^{11} x^{18}+72985 m^{9} x^{20}+3889578 m^{7} x^{22}+6875 m^{10} x^{18}+2271555 m^{8} x^{20}+51069018 m^{6} x^{22}+165 m^{11} x^{16}+376365 m^{9} x^{18}+45134958 m^{7} x^{20}+453714470 m^{5} x^{22}+20955 m^{10} x^{16}+11870265 m^{8} x^{18}+597988314 m^{6} x^{20}+2702025590 m^{4} x^{22}+330 m^{11} x^{14}+1164735 m^{9} x^{16}+238653030 m^{7} x^{18}+5353566130 m^{5} x^{20}+10431670821 m^{3} x^{22}+42570 m^{10} x^{14}+37263105 m^{8} x^{16}+3194704590 m^{6} x^{18}+32087153670 m^{4} x^{20}+24372200061 m^{2} x^{22}+462 m^{11} x^{12}+2403390 m^{9} x^{14}+759091410 m^{7} x^{16}+28857216410 m^{5} x^{18}+124530626231 m^{3} x^{20}+29985521895 m \,x^{22}+60522 m^{10} x^{12}+78076350 m^{8} x^{14}+10282782510 m^{6} x^{16}+174273100210 m^{4} x^{18}+292163767533 m^{2} x^{20}+13749310575 x^{22}+462 m^{11} x^{10}+3471930 m^{9} x^{12}+1613983140 m^{7} x^{14}+93862508190 m^{5} x^{16}+680615362515 m^{3} x^{18}+360568238085 m \,x^{20}+61446 m^{10} x^{10}+114642990 m^{8} x^{12}+22164925860 m^{6} x^{14}+572017996770 m^{4} x^{16}+1604842704135 m^{2} x^{18}+165646455975 x^{20}+330 m^{11} x^{8}+3582810 m^{9} x^{10}+2408820876 m^{7} x^{12}+204865733820 m^{5} x^{14}+2251106854425 m^{3} x^{16}+1988025402825 m \,x^{18}+44550 m^{10} x^{8}+120367170 m^{8} x^{10}+33609870756 m^{6} x^{12}+1262375264700 m^{4} x^{14}+5340787250535 m^{2} x^{16}+915414625125 x^{18}+165 m^{11} x^{6}+2640990 m^{9} x^{8}+2575140876 m^{7} x^{10}+315347150580 m^{5} x^{12}+5015196628530 m^{3} x^{14}+6646727085075 m \,x^{16}+22605 m^{10} x^{6}+90358290 m^{8} x^{8}+36597992508 m^{6} x^{10}+1969992823260 m^{4} x^{12}+11991258123570 m^{2} x^{14}+3069331390125 x^{16}+55 m^{11} x^{4}+1362735 m^{9} x^{6}+1971903780 m^{7} x^{8}+349697552820 m^{5} x^{10}+7921249136262 m^{3} x^{12}+15011348834790 m \,x^{14}+7645 m^{10} x^{4}+47524455 m^{8} x^{6}+28627538940 m^{6} x^{8}+2222832699780 m^{4} x^{10}+19130651800722 m^{2} x^{12}+6957151150950 x^{14}+11 m^{11} x^{2}+468765 m^{9} x^{4}+1059893010 m^{7} x^{6}+279691771260 m^{5} x^{8}+9079996141062 m^{3} x^{10}+24133835554290 m \,x^{12}+1551 m^{10} x^{2}+16677375 m^{8} x^{4}+15768085410 m^{6} x^{6}+1818135330660 m^{4} x^{8}+22226933020446 m^{2} x^{10}+11238474936150 x^{12}+m^{11}+96745 m^{9} x^{2}+380801190 m^{7} x^{4}+158293212990 m^{5} x^{6}+7587607623090 m^{3} x^{8}+28336045738770 m \,x^{10}+143 m^{10}+3514005 m^{8} x^{2}+5825106210 m^{6} x^{4}+1059628145070 m^{4} x^{6}+18930738943710 m^{2} x^{8}+13281834015450 x^{10}+9075 m^{9}+82295598 m^{7} x^{2}+60431072570 m^{5} x^{4}+4558015784025 m^{3} x^{6}+24503570194950 m \,x^{8}+336765 m^{8}+1298935638 m^{6} x^{2}+420404849150 m^{4} x^{4}+11703493287585 m^{2} x^{6}+11595251918250 x^{8}+8103018 m^{7}+14014513810 m^{5} x^{2}+1889780020755 m^{3} x^{4}+15515657331075 m \,x^{6}+132426294 m^{6}+102468500970 m^{4} x^{2}+5087634488145 m^{2} x^{4}+7454090518875 x^{6}+1495875590 m^{5}+490955350391 m^{3} x^{2}+7041864340665 m \,x^{4}+11641582810 m^{4}+1434440867211 m^{2} x^{2}+3478575575475 x^{4}+60936676581 m^{3}+2192684754645 m \,x^{2}+203363952363 m^{2}+1159525191825 x^{2}+387182170935 m +316234143225\right) x \left(f x \right)^{m}}{\left(m +1\right) \left(m +3\right) \left(m +5\right) \left(m +7\right) \left(m +9\right) \left(m +11\right) \left(m +13\right) \left(m +15\right) \left(m +17\right) \left(m +19\right) \left(m +21\right) \left(m +23\right)}"," ",0,"(f*x)^m*(m^11*x^22+121*m^10*x^22+11*m^11*x^20+6435*m^9*x^22+1353*m^10*x^20+197835*m^8*x^22+55*m^11*x^18+72985*m^9*x^20+3889578*m^7*x^22+6875*m^10*x^18+2271555*m^8*x^20+51069018*m^6*x^22+165*m^11*x^16+376365*m^9*x^18+45134958*m^7*x^20+453714470*m^5*x^22+20955*m^10*x^16+11870265*m^8*x^18+597988314*m^6*x^20+2702025590*m^4*x^22+330*m^11*x^14+1164735*m^9*x^16+238653030*m^7*x^18+5353566130*m^5*x^20+10431670821*m^3*x^22+42570*m^10*x^14+37263105*m^8*x^16+3194704590*m^6*x^18+32087153670*m^4*x^20+24372200061*m^2*x^22+462*m^11*x^12+2403390*m^9*x^14+759091410*m^7*x^16+28857216410*m^5*x^18+124530626231*m^3*x^20+29985521895*m*x^22+60522*m^10*x^12+78076350*m^8*x^14+10282782510*m^6*x^16+174273100210*m^4*x^18+292163767533*m^2*x^20+13749310575*x^22+462*m^11*x^10+3471930*m^9*x^12+1613983140*m^7*x^14+93862508190*m^5*x^16+680615362515*m^3*x^18+360568238085*m*x^20+61446*m^10*x^10+114642990*m^8*x^12+22164925860*m^6*x^14+572017996770*m^4*x^16+1604842704135*m^2*x^18+165646455975*x^20+330*m^11*x^8+3582810*m^9*x^10+2408820876*m^7*x^12+204865733820*m^5*x^14+2251106854425*m^3*x^16+1988025402825*m*x^18+44550*m^10*x^8+120367170*m^8*x^10+33609870756*m^6*x^12+1262375264700*m^4*x^14+5340787250535*m^2*x^16+915414625125*x^18+165*m^11*x^6+2640990*m^9*x^8+2575140876*m^7*x^10+315347150580*m^5*x^12+5015196628530*m^3*x^14+6646727085075*m*x^16+22605*m^10*x^6+90358290*m^8*x^8+36597992508*m^6*x^10+1969992823260*m^4*x^12+11991258123570*m^2*x^14+3069331390125*x^16+55*m^11*x^4+1362735*m^9*x^6+1971903780*m^7*x^8+349697552820*m^5*x^10+7921249136262*m^3*x^12+15011348834790*m*x^14+7645*m^10*x^4+47524455*m^8*x^6+28627538940*m^6*x^8+2222832699780*m^4*x^10+19130651800722*m^2*x^12+6957151150950*x^14+11*m^11*x^2+468765*m^9*x^4+1059893010*m^7*x^6+279691771260*m^5*x^8+9079996141062*m^3*x^10+24133835554290*m*x^12+1551*m^10*x^2+16677375*m^8*x^4+15768085410*m^6*x^6+1818135330660*m^4*x^8+22226933020446*m^2*x^10+11238474936150*x^12+m^11+96745*m^9*x^2+380801190*m^7*x^4+158293212990*m^5*x^6+7587607623090*m^3*x^8+28336045738770*m*x^10+143*m^10+3514005*m^8*x^2+5825106210*m^6*x^4+1059628145070*m^4*x^6+18930738943710*m^2*x^8+13281834015450*x^10+9075*m^9+82295598*m^7*x^2+60431072570*m^5*x^4+4558015784025*m^3*x^6+24503570194950*m*x^8+336765*m^8+1298935638*m^6*x^2+420404849150*m^4*x^4+11703493287585*m^2*x^6+11595251918250*x^8+8103018*m^7+14014513810*m^5*x^2+1889780020755*m^3*x^4+15515657331075*m*x^6+132426294*m^6+102468500970*m^4*x^2+5087634488145*m^2*x^4+7454090518875*x^6+1495875590*m^5+490955350391*m^3*x^2+7041864340665*m*x^4+11641582810*m^4+1434440867211*m^2*x^2+3478575575475*x^4+60936676581*m^3+2192684754645*m*x^2+203363952363*m^2+1159525191825*x^2+387182170935*m+316234143225)*x/(m+1)/(m+3)/(m+5)/(m+7)/(m+9)/(m+11)/(m+13)/(m+15)/(m+17)/(m+19)/(m+21)/(m+23)","B"
66,1,62,28,0.001000," ","int(x^5*(x^2+1)*(x^4+2*x^2+1)^5,x)","\frac{1}{28} x^{28}+\frac{11}{26} x^{26}+\frac{55}{24} x^{24}+\frac{15}{2} x^{22}+\frac{33}{2} x^{20}+\frac{77}{3} x^{18}+\frac{231}{8} x^{16}+\frac{165}{7} x^{14}+\frac{55}{4} x^{12}+\frac{11}{2} x^{10}+\frac{11}{8} x^{8}+\frac{1}{6} x^{6}"," ",0,"1/28*x^28+11/26*x^26+55/24*x^24+15/2*x^22+33/2*x^20+77/3*x^18+231/8*x^16+165/7*x^14+55/4*x^12+11/2*x^10+11/8*x^8+1/6*x^6","B"
67,1,62,61,0.003000," ","int(x^4*(x^2+1)*(x^4+2*x^2+1)^5,x)","\frac{1}{27} x^{27}+\frac{11}{25} x^{25}+\frac{55}{23} x^{23}+\frac{55}{7} x^{21}+\frac{330}{19} x^{19}+\frac{462}{17} x^{17}+\frac{154}{5} x^{15}+\frac{330}{13} x^{13}+15 x^{11}+\frac{55}{9} x^{9}+\frac{11}{7} x^{7}+\frac{1}{5} x^{5}"," ",0,"1/5*x^5+11/7*x^7+55/9*x^9+15*x^11+330/13*x^13+154/5*x^15+462/17*x^17+330/19*x^19+55/7*x^21+55/23*x^23+11/25*x^25+1/27*x^27","A"
68,1,62,19,0.001000," ","int(x^3*(x^2+1)*(x^4+2*x^2+1)^5,x)","\frac{1}{26} x^{26}+\frac{11}{24} x^{24}+\frac{5}{2} x^{22}+\frac{33}{4} x^{20}+\frac{55}{3} x^{18}+\frac{231}{8} x^{16}+33 x^{14}+\frac{55}{2} x^{12}+\frac{33}{2} x^{10}+\frac{55}{8} x^{8}+\frac{11}{6} x^{6}+\frac{1}{4} x^{4}"," ",0,"1/26*x^26+11/24*x^24+5/2*x^22+33/4*x^20+55/3*x^18+231/8*x^16+33*x^14+55/2*x^12+33/2*x^10+55/8*x^8+11/6*x^6+1/4*x^4","B"
69,1,62,61,0.000000," ","int(x^2*(x^2+1)*(x^4+2*x^2+1)^5,x)","\frac{1}{25} x^{25}+\frac{11}{23} x^{23}+\frac{55}{21} x^{21}+\frac{165}{19} x^{19}+\frac{330}{17} x^{17}+\frac{154}{5} x^{15}+\frac{462}{13} x^{13}+30 x^{11}+\frac{55}{3} x^{9}+\frac{55}{7} x^{7}+\frac{11}{5} x^{5}+\frac{1}{3} x^{3}"," ",0,"1/3*x^3+11/5*x^5+55/7*x^7+55/3*x^9+30*x^11+462/13*x^13+154/5*x^15+330/17*x^17+165/19*x^19+55/21*x^21+11/23*x^23+1/25*x^25","A"
70,1,62,9,0.001000," ","int(x*(x^2+1)*(x^4+2*x^2+1)^5,x)","\frac{1}{24} x^{24}+\frac{1}{2} x^{22}+\frac{11}{4} x^{20}+\frac{55}{6} x^{18}+\frac{165}{8} x^{16}+33 x^{14}+\frac{77}{2} x^{12}+33 x^{10}+\frac{165}{8} x^{8}+\frac{55}{6} x^{6}+\frac{11}{4} x^{4}+\frac{1}{2} x^{2}"," ",0,"1/24*x^24+1/2*x^22+11/4*x^20+55/6*x^18+165/8*x^16+33*x^14+77/2*x^12+33*x^10+165/8*x^8+55/6*x^6+11/4*x^4+1/2*x^2","B"
71,1,58,57,0.001000," ","int((x^2+1)*(x^4+2*x^2+1)^5,x)","\frac{1}{23} x^{23}+\frac{11}{21} x^{21}+\frac{55}{19} x^{19}+\frac{165}{17} x^{17}+22 x^{15}+\frac{462}{13} x^{13}+42 x^{11}+\frac{110}{3} x^{9}+\frac{165}{7} x^{7}+11 x^{5}+\frac{11}{3} x^{3}+x"," ",0,"x+11/3*x^3+11*x^5+165/7*x^7+110/3*x^9+42*x^11+462/13*x^13+22*x^15+165/17*x^17+55/19*x^19+11/21*x^21+1/23*x^23","A"
72,1,59,58,0.003000," ","int((x^2+1)*(x^4+2*x^2+1)^5/x,x)","\frac{x^{22}}{22}+\frac{11 x^{20}}{20}+\frac{55 x^{18}}{18}+\frac{165 x^{16}}{16}+\frac{165 x^{14}}{7}+\frac{77 x^{12}}{2}+\frac{231 x^{10}}{5}+\frac{165 x^{8}}{4}+\frac{55 x^{6}}{2}+\frac{55 x^{4}}{4}+\frac{11 x^{2}}{2}+\ln \left(x \right)"," ",0,"11/2*x^2+55/4*x^4+55/2*x^6+165/4*x^8+231/5*x^10+77/2*x^12+165/7*x^14+165/16*x^16+55/18*x^18+11/20*x^20+1/22*x^22+ln(x)","A"
73,1,60,59,0.004000," ","int((x^2+1)*(x^4+2*x^2+1)^5/x^2,x)","\frac{x^{21}}{21}+\frac{11 x^{19}}{19}+\frac{55 x^{17}}{17}+11 x^{15}+\frac{330 x^{13}}{13}+42 x^{11}+\frac{154 x^{9}}{3}+\frac{330 x^{7}}{7}+33 x^{5}+\frac{55 x^{3}}{3}+11 x -\frac{1}{x}"," ",0,"-1/x+11*x+55/3*x^3+33*x^5+330/7*x^7+154/3*x^9+42*x^11+330/13*x^13+11*x^15+55/17*x^17+11/19*x^19+1/21*x^21","A"
74,1,61,60,0.005000," ","int((x^2+1)*(x^4+2*x^2+1)^5/x^3,x)","\frac{x^{20}}{20}+\frac{11 x^{18}}{18}+\frac{55 x^{16}}{16}+\frac{165 x^{14}}{14}+\frac{55 x^{12}}{2}+\frac{231 x^{10}}{5}+\frac{231 x^{8}}{4}+55 x^{6}+\frac{165 x^{4}}{4}+\frac{55 x^{2}}{2}+11 \ln \left(x \right)-\frac{1}{2 x^{2}}"," ",0,"-1/2/x^2+55/2*x^2+165/4*x^4+55*x^6+231/4*x^8+231/5*x^10+55/2*x^12+165/14*x^14+55/16*x^16+11/18*x^18+1/20*x^20+11*ln(x)","A"
75,1,90,102,0.039000," ","int(x^2*(e*x^2+d)/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(\sqrt{a b}\, b e \,x^{3}+3 a^{2} e \arctan \left(\frac{b x}{\sqrt{a b}}\right)-3 a b d \arctan \left(\frac{b x}{\sqrt{a b}}\right)-3 \sqrt{a b}\, a e x +3 \sqrt{a b}\, b d x \right)}{3 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, \sqrt{a b}\, b^{2}}"," ",0,"1/3*(b*x^2+a)*((a*b)^(1/2)*x^3*b*e+3*arctan(b*x/(a*b)^(1/2))*a^2*e-3*arctan(b*x/(a*b)^(1/2))*a*b*d-3*(a*b)^(1/2)*x*a*e+3*(a*b)^(1/2)*x*b*d)/((b*x^2+a)^2)^(1/2)/b^2/(a*b)^(1/2)","A"
76,1,55,57,0.010000," ","int(x*(e*x^2+d)/((b*x^2+a)^2)^(1/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(-b e \,x^{2}+a e \ln \left(b \,x^{2}+a \right)-b d \ln \left(b \,x^{2}+a \right)\right)}{2 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, b^{2}}"," ",0,"-1/2*(b*x^2+a)*(-x^2*e*b+ln(b*x^2+a)*a*e-ln(b*x^2+a)*b*d)/((b*x^2+a)^2)^(1/2)/b^2","A"
77,1,62,67,0.007000," ","int((e*x^2+d)/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(-a e \arctan \left(\frac{b x}{\sqrt{a b}}\right)+b d \arctan \left(\frac{b x}{\sqrt{a b}}\right)+\sqrt{a b}\, e x \right)}{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \sqrt{a b}\, b}"," ",0,"(b*x^2+a)*(e*x*(a*b)^(1/2)-arctan(1/(a*b)^(1/2)*b*x)*a*e+arctan(1/(a*b)^(1/2)*b*x)*b*d)/((b*x^2+a)^2)^(1/2)/b/(a*b)^(1/2)","A"
78,1,57,68,0.010000," ","int((e*x^2+d)/x/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(a e \ln \left(b \,x^{2}+a \right)+2 b d \ln \left(x \right)-b d \ln \left(b \,x^{2}+a \right)\right)}{2 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, a b}"," ",0,"1/2*(b*x^2+a)*(2*d*ln(x)*b+a*e*ln(b*x^2+a)-b*d*ln(b*x^2+a))/((b*x^2+a)^2)^(1/2)/a/b","A"
79,1,67,71,0.010000," ","int((e*x^2+d)/x^2/((b*x^2+a)^2)^(1/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(-a e x \arctan \left(\frac{b x}{\sqrt{a b}}\right)+b d x \arctan \left(\frac{b x}{\sqrt{a b}}\right)+\sqrt{a b}\, d \right)}{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \sqrt{a b}\, a x}"," ",0,"-(b*x^2+a)*(-arctan(1/(a*b)^(1/2)*b*x)*x*a*e+arctan(1/(a*b)^(1/2)*b*x)*x*b*d+d*(a*b)^(1/2))/((b*x^2+a)^2)^(1/2)/a/x/(a*b)^(1/2)","A"
80,1,79,100,0.013000," ","int((e*x^2+d)/x^3/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(2 a e \,x^{2} \ln \left(x \right)-a e \,x^{2} \ln \left(b \,x^{2}+a \right)-2 b d \,x^{2} \ln \left(x \right)+b d \,x^{2} \ln \left(b \,x^{2}+a \right)-a d \right)}{2 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, a^{2} x^{2}}"," ",0,"1/2*(b*x^2+a)*(2*ln(x)*x^2*a*e-2*ln(x)*x^2*b*d-ln(b*x^2+a)*x^2*a*e+ln(b*x^2+a)*x^2*b*d-a*d)/((b*x^2+a)^2)^(1/2)/x^2/a^2","A"
81,1,188,106,0.019000," ","int(x^2*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","-\frac{\left(-3 a \,b^{2} e \,x^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-b^{3} d \,x^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-6 a^{2} b e \,x^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-2 a \,b^{2} d \,x^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+5 \sqrt{a b}\, a b e \,x^{3}-\sqrt{a b}\, b^{2} d \,x^{3}-3 a^{3} e \arctan \left(\frac{b x}{\sqrt{a b}}\right)-a^{2} b d \arctan \left(\frac{b x}{\sqrt{a b}}\right)+3 \sqrt{a b}\, a^{2} e x +\sqrt{a b}\, a b d x \right) \left(b \,x^{2}+a \right)}{8 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a \,b^{2}}"," ",0,"-1/8*(-3*arctan(1/(a*b)^(1/2)*b*x)*x^4*a*b^2*e-arctan(1/(a*b)^(1/2)*b*x)*x^4*b^3*d+5*(a*b)^(1/2)*x^3*a*b*e-(a*b)^(1/2)*x^3*b^2*d-6*arctan(1/(a*b)^(1/2)*b*x)*x^2*a^2*b*e-2*arctan(1/(a*b)^(1/2)*b*x)*x^2*a*b^2*d+3*(a*b)^(1/2)*x*a^2*e+(a*b)^(1/2)*x*a*b*d-3*arctan(1/(a*b)^(1/2)*b*x)*a^3*e-arctan(1/(a*b)^(1/2)*b*x)*a^2*b*d)*(b*x^2+a)/(a*b)^(1/2)/a/b^2/((b*x^2+a)^2)^(3/2)","A"
82,1,38,51,0.007000," ","int(x*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(2 b e \,x^{2}+a e +b d \right)}{4 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} b^{2}}"," ",0,"-1/4*(b*x^2+a)*(2*b*e*x^2+a*e+b*d)/b^2/((b*x^2+a)^2)^(3/2)","A"
83,1,186,109,0.014000," ","int((e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(a \,b^{2} e \,x^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+3 b^{3} d \,x^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+2 a^{2} b e \,x^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+6 a \,b^{2} d \,x^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+\sqrt{a b}\, a b e \,x^{3}+3 \sqrt{a b}\, b^{2} d \,x^{3}+a^{3} e \arctan \left(\frac{b x}{\sqrt{a b}}\right)+3 a^{2} b d \arctan \left(\frac{b x}{\sqrt{a b}}\right)-\sqrt{a b}\, a^{2} e x +5 \sqrt{a b}\, a b d x \right) \left(b \,x^{2}+a \right)}{8 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{2} b}"," ",0,"1/8*(a*b^2*e*x^4*arctan(1/(a*b)^(1/2)*b*x)+3*b^3*d*x^4*arctan(1/(a*b)^(1/2)*b*x)+(a*b)^(1/2)*a*b*e*x^3+3*(a*b)^(1/2)*b^2*d*x^3+2*a^2*b*e*x^2*arctan(1/(a*b)^(1/2)*b*x)+6*a*b^2*d*x^2*arctan(1/(a*b)^(1/2)*b*x)-(a*b)^(1/2)*a^2*e*x+5*(a*b)^(1/2)*a*b*d*x+a^3*e*arctan(1/(a*b)^(1/2)*b*x)+3*a^2*b*d*arctan(1/(a*b)^(1/2)*b*x))*(b*x^2+a)/(a*b)^(1/2)/b/a^2/((b*x^2+a)^2)^(3/2)","A"
84,1,133,111,0.021000," ","int((e*x^2+d)/x/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(4 b^{3} d \,x^{4} \ln \left(x \right)-2 b^{3} d \,x^{4} \ln \left(b \,x^{2}+a \right)+8 a \,b^{2} d \,x^{2} \ln \left(x \right)-4 a \,b^{2} d \,x^{2} \ln \left(b \,x^{2}+a \right)+2 a \,b^{2} d \,x^{2}+4 a^{2} b d \ln \left(x \right)-2 a^{2} b d \ln \left(b \,x^{2}+a \right)-a^{3} e +3 a^{2} b d \right) \left(b \,x^{2}+a \right)}{4 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{3} b}"," ",0,"1/4*(4*ln(x)*x^4*b^3*d-2*ln(b*x^2+a)*x^4*b^3*d+8*ln(x)*x^2*a*b^2*d-4*ln(b*x^2+a)*x^2*a*b^2*d+2*b^2*d*x^2*a+4*ln(x)*a^2*b*d-2*ln(b*x^2+a)*a^2*b*d-a^3*e+3*a^2*b*d)*(b*x^2+a)/b/a^3/((b*x^2+a)^2)^(3/2)","A"
85,1,206,132,0.023000," ","int((e*x^2+d)/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(3 a \,b^{2} e \,x^{5} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-15 b^{3} d \,x^{5} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+6 a^{2} b e \,x^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-30 a \,b^{2} d \,x^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+3 \sqrt{a b}\, a b e \,x^{4}-15 \sqrt{a b}\, b^{2} d \,x^{4}+3 a^{3} e x \arctan \left(\frac{b x}{\sqrt{a b}}\right)-15 a^{2} b d x \arctan \left(\frac{b x}{\sqrt{a b}}\right)+5 \sqrt{a b}\, a^{2} e \,x^{2}-25 \sqrt{a b}\, a b d \,x^{2}-8 \sqrt{a b}\, a^{2} d \right) \left(b \,x^{2}+a \right)}{8 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{3} x}"," ",0,"1/8*(3*arctan(1/(a*b)^(1/2)*b*x)*x^5*a*b^2*e-15*arctan(1/(a*b)^(1/2)*b*x)*x^5*b^3*d+3*(a*b)^(1/2)*x^4*a*b*e-15*(a*b)^(1/2)*x^4*b^2*d+6*arctan(1/(a*b)^(1/2)*b*x)*x^3*a^2*b*e-30*arctan(1/(a*b)^(1/2)*b*x)*x^3*a*b^2*d+5*(a*b)^(1/2)*x^2*a^2*e-25*(a*b)^(1/2)*x^2*a*b*d+3*arctan(1/(a*b)^(1/2)*b*x)*x*a^3*e-15*arctan(1/(a*b)^(1/2)*b*x)*x*a^2*b*d-8*(a*b)^(1/2)*a^2*d)*(b*x^2+a)/(a*b)^(1/2)/x/a^3/((b*x^2+a)^2)^(3/2)","A"
86,1,249,159,0.025000," ","int((e*x^2+d)/x^3/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(4 a \,b^{2} e \,x^{6} \ln \left(x \right)-2 a \,b^{2} e \,x^{6} \ln \left(b \,x^{2}+a \right)-12 b^{3} d \,x^{6} \ln \left(x \right)+6 b^{3} d \,x^{6} \ln \left(b \,x^{2}+a \right)+8 a^{2} b e \,x^{4} \ln \left(x \right)-4 a^{2} b e \,x^{4} \ln \left(b \,x^{2}+a \right)-24 a \,b^{2} d \,x^{4} \ln \left(x \right)+12 a \,b^{2} d \,x^{4} \ln \left(b \,x^{2}+a \right)+2 a^{2} b e \,x^{4}-6 a \,b^{2} d \,x^{4}+4 a^{3} e \,x^{2} \ln \left(x \right)-2 a^{3} e \,x^{2} \ln \left(b \,x^{2}+a \right)-12 a^{2} b d \,x^{2} \ln \left(x \right)+6 a^{2} b d \,x^{2} \ln \left(b \,x^{2}+a \right)+3 a^{3} e \,x^{2}-9 a^{2} b d \,x^{2}-2 a^{3} d \right) \left(b \,x^{2}+a \right)}{4 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{4} x^{2}}"," ",0,"1/4*(4*ln(x)*x^6*a*b^2*e-12*ln(x)*x^6*b^3*d-2*ln(b*x^2+a)*x^6*a*b^2*e+6*ln(b*x^2+a)*x^6*b^3*d+8*ln(x)*x^4*a^2*b*e-24*ln(x)*x^4*a*b^2*d-4*ln(b*x^2+a)*x^4*a^2*b*e+12*ln(b*x^2+a)*x^4*a*b^2*d+2*x^4*a^2*b*e-6*x^4*a*b^2*d+4*ln(x)*x^2*a^3*e-12*ln(x)*x^2*a^2*b*d-2*ln(b*x^2+a)*x^2*a^3*e+6*ln(b*x^2+a)*x^2*a^2*b*d+3*x^2*a^3*e-9*x^2*a^2*b*d-2*a^3*d)*(b*x^2+a)/x^2/a^4/((b*x^2+a)^2)^(3/2)","A"
87,1,1099,323,0.010000," ","int((f*x)^m*(e*x^2+d)*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(b^{5} e \,m^{6} x^{12}+36 b^{5} e \,m^{5} x^{12}+5 a \,b^{4} e \,m^{6} x^{10}+b^{5} d \,m^{6} x^{10}+505 b^{5} e \,m^{4} x^{12}+190 a \,b^{4} e \,m^{5} x^{10}+38 b^{5} d \,m^{5} x^{10}+3480 b^{5} e \,m^{3} x^{12}+10 a^{2} b^{3} e \,m^{6} x^{8}+5 a \,b^{4} d \,m^{6} x^{8}+2775 a \,b^{4} e \,m^{4} x^{10}+555 b^{5} d \,m^{4} x^{10}+12139 b^{5} e \,m^{2} x^{12}+400 a^{2} b^{3} e \,m^{5} x^{8}+200 a \,b^{4} d \,m^{5} x^{8}+19700 a \,b^{4} e \,m^{3} x^{10}+3940 b^{5} d \,m^{3} x^{10}+19524 b^{5} e m \,x^{12}+10 a^{3} b^{2} e \,m^{6} x^{6}+10 a^{2} b^{3} d \,m^{6} x^{6}+6130 a^{2} b^{3} e \,m^{4} x^{8}+3065 a \,b^{4} d \,m^{4} x^{8}+70195 a \,b^{4} e \,m^{2} x^{10}+14039 b^{5} d \,m^{2} x^{10}+10395 e \,b^{5} x^{12}+420 a^{3} b^{2} e \,m^{5} x^{6}+420 a^{2} b^{3} d \,m^{5} x^{6}+45280 a^{2} b^{3} e \,m^{3} x^{8}+22640 a \,b^{4} d \,m^{3} x^{8}+114510 a \,b^{4} e m \,x^{10}+22902 b^{5} d m \,x^{10}+5 a^{4} b e \,m^{6} x^{4}+10 a^{3} b^{2} d \,m^{6} x^{4}+6790 a^{3} b^{2} e \,m^{4} x^{6}+6790 a^{2} b^{3} d \,m^{4} x^{6}+166270 a^{2} b^{3} e \,m^{2} x^{8}+83135 a \,b^{4} d \,m^{2} x^{8}+61425 a \,b^{4} e \,x^{10}+12285 b^{5} d \,x^{10}+220 a^{4} b e \,m^{5} x^{4}+440 a^{3} b^{2} d \,m^{5} x^{4}+52920 a^{3} b^{2} e \,m^{3} x^{6}+52920 a^{2} b^{3} d \,m^{3} x^{6}+276880 a^{2} b^{3} e m \,x^{8}+138440 a \,b^{4} d m \,x^{8}+a^{5} e \,m^{6} x^{2}+5 a^{4} b d \,m^{6} x^{2}+3765 a^{4} b e \,m^{4} x^{4}+7530 a^{3} b^{2} d \,m^{4} x^{4}+203350 a^{3} b^{2} e \,m^{2} x^{6}+203350 a^{2} b^{3} d \,m^{2} x^{6}+150150 a^{2} b^{3} e \,x^{8}+75075 a \,b^{4} d \,x^{8}+46 a^{5} e \,m^{5} x^{2}+230 a^{4} b d \,m^{5} x^{2}+31400 a^{4} b e \,m^{3} x^{4}+62800 a^{3} b^{2} d \,m^{3} x^{4}+349860 a^{3} b^{2} e m \,x^{6}+349860 a^{2} b^{3} d m \,x^{6}+a^{5} d \,m^{6}+835 a^{5} e \,m^{4} x^{2}+4175 a^{4} b d \,m^{4} x^{2}+129895 a^{4} b e \,m^{2} x^{4}+259790 a^{3} b^{2} d \,m^{2} x^{4}+193050 a^{3} b^{2} e \,x^{6}+193050 a^{2} b^{3} d \,x^{6}+48 a^{5} d \,m^{5}+7540 a^{5} e \,m^{3} x^{2}+37700 a^{4} b d \,m^{3} x^{2}+237180 a^{4} b e m \,x^{4}+474360 a^{3} b^{2} d m \,x^{4}+925 a^{5} d \,m^{4}+34759 a^{5} e \,m^{2} x^{2}+173795 a^{4} b d \,m^{2} x^{2}+135135 a^{4} b e \,x^{4}+270270 a^{3} b^{2} d \,x^{4}+9120 a^{5} d \,m^{3}+73054 a^{5} e m \,x^{2}+365270 a^{4} b d m \,x^{2}+48259 a^{5} d \,m^{2}+45045 a^{5} e \,x^{2}+225225 a^{4} b d \,x^{2}+129072 a^{5} d m +135135 d \,a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x \left(f x \right)^{m}}{\left(m +13\right) \left(m +11\right) \left(m +9\right) \left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right) \left(b \,x^{2}+a \right)^{5}}"," ",0,"x*(b^5*e*m^6*x^12+36*b^5*e*m^5*x^12+5*a*b^4*e*m^6*x^10+b^5*d*m^6*x^10+505*b^5*e*m^4*x^12+190*a*b^4*e*m^5*x^10+38*b^5*d*m^5*x^10+3480*b^5*e*m^3*x^12+10*a^2*b^3*e*m^6*x^8+5*a*b^4*d*m^6*x^8+2775*a*b^4*e*m^4*x^10+555*b^5*d*m^4*x^10+12139*b^5*e*m^2*x^12+400*a^2*b^3*e*m^5*x^8+200*a*b^4*d*m^5*x^8+19700*a*b^4*e*m^3*x^10+3940*b^5*d*m^3*x^10+19524*b^5*e*m*x^12+10*a^3*b^2*e*m^6*x^6+10*a^2*b^3*d*m^6*x^6+6130*a^2*b^3*e*m^4*x^8+3065*a*b^4*d*m^4*x^8+70195*a*b^4*e*m^2*x^10+14039*b^5*d*m^2*x^10+10395*b^5*e*x^12+420*a^3*b^2*e*m^5*x^6+420*a^2*b^3*d*m^5*x^6+45280*a^2*b^3*e*m^3*x^8+22640*a*b^4*d*m^3*x^8+114510*a*b^4*e*m*x^10+22902*b^5*d*m*x^10+5*a^4*b*e*m^6*x^4+10*a^3*b^2*d*m^6*x^4+6790*a^3*b^2*e*m^4*x^6+6790*a^2*b^3*d*m^4*x^6+166270*a^2*b^3*e*m^2*x^8+83135*a*b^4*d*m^2*x^8+61425*a*b^4*e*x^10+12285*b^5*d*x^10+220*a^4*b*e*m^5*x^4+440*a^3*b^2*d*m^5*x^4+52920*a^3*b^2*e*m^3*x^6+52920*a^2*b^3*d*m^3*x^6+276880*a^2*b^3*e*m*x^8+138440*a*b^4*d*m*x^8+a^5*e*m^6*x^2+5*a^4*b*d*m^6*x^2+3765*a^4*b*e*m^4*x^4+7530*a^3*b^2*d*m^4*x^4+203350*a^3*b^2*e*m^2*x^6+203350*a^2*b^3*d*m^2*x^6+150150*a^2*b^3*e*x^8+75075*a*b^4*d*x^8+46*a^5*e*m^5*x^2+230*a^4*b*d*m^5*x^2+31400*a^4*b*e*m^3*x^4+62800*a^3*b^2*d*m^3*x^4+349860*a^3*b^2*e*m*x^6+349860*a^2*b^3*d*m*x^6+a^5*d*m^6+835*a^5*e*m^4*x^2+4175*a^4*b*d*m^4*x^2+129895*a^4*b*e*m^2*x^4+259790*a^3*b^2*d*m^2*x^4+193050*a^3*b^2*e*x^6+193050*a^2*b^3*d*x^6+48*a^5*d*m^5+7540*a^5*e*m^3*x^2+37700*a^4*b*d*m^3*x^2+237180*a^4*b*e*m*x^4+474360*a^3*b^2*d*m*x^4+925*a^5*d*m^4+34759*a^5*e*m^2*x^2+173795*a^4*b*d*m^2*x^2+135135*a^4*b*e*x^4+270270*a^3*b^2*d*x^4+9120*a^5*d*m^3+73054*a^5*e*m*x^2+365270*a^4*b*d*m*x^2+48259*a^5*d*m^2+45045*a^5*e*x^2+225225*a^4*b*d*x^2+129072*a^5*d*m+135135*a^5*d)*(f*x)^m*((b*x^2+a)^2)^(5/2)/(m+13)/(m+11)/(m+9)/(m+7)/(m+5)/(m+3)/(m+1)/(b*x^2+a)^5","B"
88,1,495,221,0.009000," ","int((f*x)^m*(e*x^2+d)*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(b^{3} e \,m^{4} x^{8}+16 b^{3} e \,m^{3} x^{8}+3 a \,b^{2} e \,m^{4} x^{6}+b^{3} d \,m^{4} x^{6}+86 b^{3} e \,m^{2} x^{8}+54 a \,b^{2} e \,m^{3} x^{6}+18 b^{3} d \,m^{3} x^{6}+176 b^{3} e m \,x^{8}+3 a^{2} b e \,m^{4} x^{4}+3 a \,b^{2} d \,m^{4} x^{4}+312 a \,b^{2} e \,m^{2} x^{6}+104 b^{3} d \,m^{2} x^{6}+105 b^{3} e \,x^{8}+60 a^{2} b e \,m^{3} x^{4}+60 a \,b^{2} d \,m^{3} x^{4}+666 a \,b^{2} e m \,x^{6}+222 b^{3} d m \,x^{6}+a^{3} e \,m^{4} x^{2}+3 a^{2} b d \,m^{4} x^{2}+390 a^{2} b e \,m^{2} x^{4}+390 a \,b^{2} d \,m^{2} x^{4}+405 a \,b^{2} e \,x^{6}+135 b^{3} d \,x^{6}+22 a^{3} e \,m^{3} x^{2}+66 a^{2} b d \,m^{3} x^{2}+900 a^{2} b e m \,x^{4}+900 a \,b^{2} d m \,x^{4}+a^{3} d \,m^{4}+164 a^{3} e \,m^{2} x^{2}+492 a^{2} b d \,m^{2} x^{2}+567 a^{2} b e \,x^{4}+567 a \,b^{2} d \,x^{4}+24 a^{3} d \,m^{3}+458 a^{3} e m \,x^{2}+1374 a^{2} b d m \,x^{2}+206 a^{3} d \,m^{2}+315 a^{3} e \,x^{2}+945 a^{2} b d \,x^{2}+744 a^{3} d m +945 a^{3} d \right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x \left(f x \right)^{m}}{\left(m +9\right) \left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right) \left(b \,x^{2}+a \right)^{3}}"," ",0,"x*(b^3*e*m^4*x^8+16*b^3*e*m^3*x^8+3*a*b^2*e*m^4*x^6+b^3*d*m^4*x^6+86*b^3*e*m^2*x^8+54*a*b^2*e*m^3*x^6+18*b^3*d*m^3*x^6+176*b^3*e*m*x^8+3*a^2*b*e*m^4*x^4+3*a*b^2*d*m^4*x^4+312*a*b^2*e*m^2*x^6+104*b^3*d*m^2*x^6+105*b^3*e*x^8+60*a^2*b*e*m^3*x^4+60*a*b^2*d*m^3*x^4+666*a*b^2*e*m*x^6+222*b^3*d*m*x^6+a^3*e*m^4*x^2+3*a^2*b*d*m^4*x^2+390*a^2*b*e*m^2*x^4+390*a*b^2*d*m^2*x^4+405*a*b^2*e*x^6+135*b^3*d*x^6+22*a^3*e*m^3*x^2+66*a^2*b*d*m^3*x^2+900*a^2*b*e*m*x^4+900*a*b^2*d*m*x^4+a^3*d*m^4+164*a^3*e*m^2*x^2+492*a^2*b*d*m^2*x^2+567*a^2*b*e*x^4+567*a*b^2*d*x^4+24*a^3*d*m^3+458*a^3*e*m*x^2+1374*a^2*b*d*m*x^2+206*a^3*d*m^2+315*a^3*e*x^2+945*a^2*b*d*x^2+744*a^3*d*m+945*a^3*d)*(f*x)^m*((b*x^2+a)^2)^(3/2)/(m+9)/(m+7)/(m+5)/(m+3)/(m+1)/(b*x^2+a)^3","B"
89,1,131,120,0.006000," ","int((f*x)^m*(e*x^2+d)*(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x)","\frac{\left(b e \,m^{2} x^{4}+4 b e m \,x^{4}+a e \,m^{2} x^{2}+b d \,m^{2} x^{2}+3 b e \,x^{4}+6 a e m \,x^{2}+6 b d m \,x^{2}+a d \,m^{2}+5 a e \,x^{2}+5 b d \,x^{2}+8 a d m +15 a d \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x \left(f x \right)^{m}}{\left(m +5\right) \left(m +3\right) \left(m +1\right) \left(b \,x^{2}+a \right)}"," ",0,"x*(b*e*m^2*x^4+4*b*e*m*x^4+a*e*m^2*x^2+b*d*m^2*x^2+3*b*e*x^4+6*a*e*m*x^2+6*b*d*m*x^2+a*d*m^2+5*a*e*x^2+5*b*d*x^2+8*a*d*m+15*a*d)*(f*x)^m*((b*x^2+a)^2)^(1/2)/(m+5)/(m+3)/(m+1)/(b*x^2+a)","A"
90,0,0,110,0.094000," ","int((f*x)^m*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x)","\int \frac{\left(e \,x^{2}+d \right) \left(f x \right)^{m}}{\sqrt{b^{2} x^{4}+2 a b \,x^{2}+a^{2}}}\, dx"," ",0,"int((f*x)^m*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x)","F"
91,0,0,126,0.029000," ","int((f*x)^m*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\int \frac{\left(e \,x^{2}+d \right) \left(f x \right)^{m}}{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int((f*x)^m*(e*x^2+d)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","F"
92,1,40,32,0.002000," ","int(x*(b*x^2+a)*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","\frac{\left(b \,x^{2}+a \right)^{2} \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{4 \left(p +1\right) b}"," ",0,"1/4*(b*x^2+a)^2/b/(1+p)*(b^2*x^4+2*a*b*x^2+a^2)^p","A"
93,1,62,82,0.007000," ","int(x^3*(b*x^2+a)*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","-\frac{\left(-2 x^{2} p b -2 b \,x^{2}+a \right) \left(b \,x^{2}+a \right)^{2} \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{4 \left(2 p^{2}+5 p +3\right) b^{2}}"," ",0,"-1/4*(b^2*x^4+2*a*b*x^2+a^2)^p*(-2*b*p*x^2-2*b*x^2+a)*(b*x^2+a)^2/b^2/(2*p^2+5*p+3)","A"
94,1,99,124,0.006000," ","int(x^5*(b*x^2+a)*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","\frac{\left(b \,x^{2}+a \right)^{2} \left(2 b^{2} p^{2} x^{4}+5 b^{2} p \,x^{4}+3 b^{2} x^{4}-2 a b p \,x^{2}-2 a b \,x^{2}+a^{2}\right) \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{4 \left(2 p^{3}+9 p^{2}+13 p +6\right) b^{3}}"," ",0,"1/4*(b*x^2+a)^2*(2*b^2*p^2*x^4+5*b^2*p*x^4+3*b^2*x^4-2*a*b*p*x^2-2*a*b*x^2+a^2)*(b^2*x^4+2*a*b*x^2+a^2)^p/b^3/(2*p^3+9*p^2+13*p+6)","A"
95,1,226,150,0.000000," ","int(x^3*(B*x^2+A)*(c*x^4+b*x^2+a)^3,x)","\frac{B \,c^{3} x^{18}}{18}+\frac{\left(A \,c^{3}+3 B b \,c^{2}\right) x^{16}}{16}+\frac{\left(3 A b \,c^{2}+\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) B \right) x^{14}}{14}+\frac{\left(\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) A +\left(4 a b c +\left(2 a c +b^{2}\right) b \right) B \right) x^{12}}{12}+\frac{\left(\left(4 a b c +\left(2 a c +b^{2}\right) b \right) A +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) B \right) x^{10}}{10}+\frac{A \,a^{3} x^{4}}{4}+\frac{\left(3 B \,a^{2} b +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) A \right) x^{8}}{8}+\frac{\left(3 A \,a^{2} b +B \,a^{3}\right) x^{6}}{6}"," ",0,"1/18*B*c^3*x^18+1/16*(A*c^3+3*B*b*c^2)*x^16+1/14*(3*A*b*c^2+B*(a*c^2+2*b^2*c+c*(2*a*c+b^2)))*x^14+1/12*(A*(a*c^2+2*b^2*c+c*(2*a*c+b^2))+B*(4*a*b*c+b*(2*a*c+b^2)))*x^12+1/10*(A*(4*a*b*c+b*(2*a*c+b^2))+B*(a*(2*a*c+b^2)+2*b^2*a+c*a^2))*x^10+1/8*(A*(a*(2*a*c+b^2)+2*b^2*a+c*a^2)+3*B*a^2*b)*x^8+1/6*(3*A*a^2*b+B*a^3)*x^6+1/4*a^3*A*x^4","A"
96,1,226,150,0.000000," ","int(x^2*(B*x^2+A)*(c*x^4+b*x^2+a)^3,x)","\frac{B \,c^{3} x^{17}}{17}+\frac{\left(A \,c^{3}+3 B b \,c^{2}\right) x^{15}}{15}+\frac{\left(3 A b \,c^{2}+\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) B \right) x^{13}}{13}+\frac{\left(\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) A +\left(4 a b c +\left(2 a c +b^{2}\right) b \right) B \right) x^{11}}{11}+\frac{\left(\left(4 a b c +\left(2 a c +b^{2}\right) b \right) A +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) B \right) x^{9}}{9}+\frac{A \,a^{3} x^{3}}{3}+\frac{\left(3 B \,a^{2} b +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) A \right) x^{7}}{7}+\frac{\left(3 A \,a^{2} b +B \,a^{3}\right) x^{5}}{5}"," ",0,"1/17*B*c^3*x^17+1/15*(A*c^3+3*B*b*c^2)*x^15+1/13*(3*A*b*c^2+(a*c^2+2*b^2*c+(2*a*c+b^2)*c)*B)*x^13+1/11*((a*c^2+2*b^2*c+(2*a*c+b^2)*c)*A+(4*a*b*c+(2*a*c+b^2)*b)*B)*x^11+1/9*((4*a*b*c+(2*a*c+b^2)*b)*A+(a^2*c+2*a*b^2+(2*a*c+b^2)*a)*B)*x^9+1/7*(3*B*a^2*b+(a^2*c+2*a*b^2+(2*a*c+b^2)*a)*A)*x^7+1/5*(3*A*a^2*b+B*a^3)*x^5+1/3*a^3*A*x^3","A"
97,1,226,150,0.000000," ","int(x*(B*x^2+A)*(c*x^4+b*x^2+a)^3,x)","\frac{B \,c^{3} x^{16}}{16}+\frac{\left(A \,c^{3}+3 B b \,c^{2}\right) x^{14}}{14}+\frac{\left(3 A b \,c^{2}+\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) B \right) x^{12}}{12}+\frac{\left(\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) A +\left(4 a b c +\left(2 a c +b^{2}\right) b \right) B \right) x^{10}}{10}+\frac{\left(\left(4 a b c +\left(2 a c +b^{2}\right) b \right) A +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) B \right) x^{8}}{8}+\frac{A \,a^{3} x^{2}}{2}+\frac{\left(3 B \,a^{2} b +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) A \right) x^{6}}{6}+\frac{\left(3 A \,a^{2} b +B \,a^{3}\right) x^{4}}{4}"," ",0,"1/16*B*c^3*x^16+1/14*(A*c^3+3*B*b*c^2)*x^14+1/12*(3*A*b*c^2+(a*c^2+2*b^2*c+(2*a*c+b^2)*c)*B)*x^12+1/10*((a*c^2+2*b^2*c+(2*a*c+b^2)*c)*A+(4*a*b*c+(2*a*c+b^2)*b)*B)*x^10+1/8*((4*a*b*c+(2*a*c+b^2)*b)*A+(a^2*c+2*a*b^2+(2*a*c+b^2)*a)*B)*x^8+1/6*(3*B*a^2*b+(a^2*c+2*a*b^2+(2*a*c+b^2)*a)*A)*x^6+1/4*(3*A*a^2*b+B*a^3)*x^4+1/2*a^3*A*x^2","A"
98,1,223,147,0.000000," ","int((B*x^2+A)*(c*x^4+b*x^2+a)^3,x)","\frac{B \,c^{3} x^{15}}{15}+\frac{\left(A \,c^{3}+3 B b \,c^{2}\right) x^{13}}{13}+\frac{\left(3 A b \,c^{2}+\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) B \right) x^{11}}{11}+\frac{\left(\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) A +\left(4 a b c +\left(2 a c +b^{2}\right) b \right) B \right) x^{9}}{9}+\frac{\left(\left(4 a b c +\left(2 a c +b^{2}\right) b \right) A +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) B \right) x^{7}}{7}+A \,a^{3} x +\frac{\left(3 B \,a^{2} b +\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) A \right) x^{5}}{5}+\frac{\left(3 A \,a^{2} b +B \,a^{3}\right) x^{3}}{3}"," ",0,"1/15*B*c^3*x^15+1/13*(A*c^3+3*B*b*c^2)*x^13+1/11*(3*A*b*c^2+(a*c^2+2*b^2*c+(2*a*c+b^2)*c)*B)*x^11+1/9*((a*c^2+2*b^2*c+(2*a*c+b^2)*c)*A+(4*a*b*c+(2*a*c+b^2)*b)*B)*x^9+1/7*((4*a*b*c+(2*a*c+b^2)*b)*A+(a^2*c+2*a*b^2+(2*a*c+b^2)*a)*B)*x^7+1/5*(3*B*a^2*b+(a^2*c+2*a*b^2+(2*a*c+b^2)*a)*A)*x^5+1/3*(3*A*a^2*b+B*a^3)*x^3+a^3*A*x","A"
99,1,191,148,0.005000," ","int((B*x^2+A)*(c*x^4+b*x^2+a)^3/x,x)","\frac{B \,c^{3} x^{14}}{14}+\frac{A \,c^{3} x^{12}}{12}+\frac{B b \,c^{2} x^{12}}{4}+\frac{3 A b \,c^{2} x^{10}}{10}+\frac{3 B a \,c^{2} x^{10}}{10}+\frac{3 B \,b^{2} c \,x^{10}}{10}+\frac{3 A a \,c^{2} x^{8}}{8}+\frac{3 A \,b^{2} c \,x^{8}}{8}+\frac{3 B a b c \,x^{8}}{4}+\frac{B \,b^{3} x^{8}}{8}+A a b c \,x^{6}+\frac{A \,b^{3} x^{6}}{6}+\frac{B \,a^{2} c \,x^{6}}{2}+\frac{B a \,b^{2} x^{6}}{2}+\frac{3 A \,a^{2} c \,x^{4}}{4}+\frac{3 A a \,b^{2} x^{4}}{4}+\frac{3 B \,a^{2} b \,x^{4}}{4}+\frac{3 A \,a^{2} b \,x^{2}}{2}+\frac{B \,a^{3} x^{2}}{2}+A \,a^{3} \ln \left(x \right)"," ",0,"1/14*B*c^3*x^14+1/12*A*x^12*c^3+1/4*B*x^12*b*c^2+3/10*A*x^10*b*c^2+3/10*B*x^10*a*c^2+3/10*B*x^10*b^2*c+3/8*A*x^8*a*c^2+3/8*A*x^8*b^2*c+3/4*B*x^8*a*b*c+1/8*B*x^8*b^3+A*x^6*a*b*c+1/6*A*x^6*b^3+1/2*B*x^6*a^2*c+1/2*B*x^6*a*b^2+3/4*A*x^4*a^2*c+3/4*A*x^4*a*b^2+3/4*B*x^4*a^2*b+3/2*A*x^2*a^2*b+1/2*B*x^2*a^3+a^3*A*ln(x)","A"
100,1,186,146,0.004000," ","int((B*x^2+A)*(c*x^4+b*x^2+a)^3/x^2,x)","\frac{B \,c^{3} x^{13}}{13}+\frac{A \,c^{3} x^{11}}{11}+\frac{3 B b \,c^{2} x^{11}}{11}+\frac{A b \,c^{2} x^{9}}{3}+\frac{B a \,c^{2} x^{9}}{3}+\frac{B \,b^{2} c \,x^{9}}{3}+\frac{3 A a \,c^{2} x^{7}}{7}+\frac{3 A \,b^{2} c \,x^{7}}{7}+\frac{6 B a b c \,x^{7}}{7}+\frac{B \,b^{3} x^{7}}{7}+\frac{6 A a b c \,x^{5}}{5}+\frac{A \,b^{3} x^{5}}{5}+\frac{3 B \,a^{2} c \,x^{5}}{5}+\frac{3 B a \,b^{2} x^{5}}{5}+A \,a^{2} c \,x^{3}+A a \,b^{2} x^{3}+B \,a^{2} b \,x^{3}+3 A \,a^{2} b x +B \,a^{3} x -\frac{A \,a^{3}}{x}"," ",0,"1/13*B*c^3*x^13+1/11*A*x^11*c^3+3/11*B*x^11*b*c^2+1/3*A*x^9*b*c^2+1/3*B*x^9*a*c^2+1/3*B*x^9*b^2*c+3/7*A*x^7*a*c^2+3/7*A*x^7*b^2*c+6/7*B*x^7*a*b*c+1/7*B*x^7*b^3+6/5*A*x^5*a*b*c+1/5*A*x^5*b^3+3/5*B*x^5*a^2*c+3/5*B*x^5*a*b^2+A*x^3*a^2*c+A*x^3*a*b^2+B*x^3*a^2*b+3*A*a^2*b*x+B*a^3*x-a^3*A/x","A"
101,1,190,148,0.007000," ","int((B*x^2+A)*(c*x^4+b*x^2+a)^3/x^3,x)","\frac{B \,c^{3} x^{12}}{12}+\frac{A \,c^{3} x^{10}}{10}+\frac{3 B b \,c^{2} x^{10}}{10}+\frac{3 A b \,c^{2} x^{8}}{8}+\frac{3 B a \,c^{2} x^{8}}{8}+\frac{3 B \,b^{2} c \,x^{8}}{8}+\frac{A a \,c^{2} x^{6}}{2}+\frac{A \,b^{2} c \,x^{6}}{2}+B a b c \,x^{6}+\frac{B \,b^{3} x^{6}}{6}+\frac{3 A a b c \,x^{4}}{2}+\frac{A \,b^{3} x^{4}}{4}+\frac{3 B \,a^{2} c \,x^{4}}{4}+\frac{3 B a \,b^{2} x^{4}}{4}+\frac{3 A \,a^{2} c \,x^{2}}{2}+\frac{3 A a \,b^{2} x^{2}}{2}+\frac{3 B \,a^{2} b \,x^{2}}{2}+3 A \,a^{2} b \ln \left(x \right)+B \,a^{3} \ln \left(x \right)-\frac{A \,a^{3}}{2 x^{2}}"," ",0,"1/12*B*c^3*x^12+1/10*A*x^10*c^3+3/10*B*x^10*b*c^2+3/8*A*x^8*b*c^2+3/8*B*x^8*a*c^2+3/8*B*x^8*b^2*c+1/2*A*x^6*a*c^2+1/2*A*x^6*b^2*c+B*x^6*a*b*c+1/6*B*x^6*b^3+3/2*A*x^4*a*b*c+1/4*A*x^4*b^3+3/4*B*x^4*a^2*c+3/4*B*x^4*a*b^2+3/2*A*x^2*a^2*c+3/2*A*x^2*a*b^2+3/2*B*x^2*a^2*b+3*A*ln(x)*a^2*b+B*ln(x)*a^3-1/2*a^3*A/x^2","A"
102,1,261,121,0.007000," ","int(x^5*(B*x^2+A)/(c*x^4+b*x^2+a),x)","\frac{B \,x^{4}}{4 c}-\frac{A a \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{A \,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{A \,x^{2}}{2 c}+\frac{3 B 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 \,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 b \,x^{2}}{2 c^{2}}-\frac{A b \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}-\frac{B a \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}+\frac{B \,b^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{3}}"," ",0,"1/4*B*x^4/c+1/2/c*A*x^2-1/2/c^2*B*x^2*b-1/4/c^2*ln(c*x^4+b*x^2+a)*A*b-1/4/c^2*ln(c*x^4+b*x^2+a)*a*B+1/4/c^3*ln(c*x^4+b*x^2+a)*b^2*B-1/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*A+3/2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b*B+1/2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*b^2-1/2/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*B","B"
103,1,175,87,0.004000," ","int(x^3*(B*x^2+A)/(c*x^4+b*x^2+a),x)","-\frac{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}-\frac{B 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 \,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{B \,x^{2}}{2 c}+\frac{A \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c}-\frac{B b \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}"," ",0,"1/2*B*x^2/c+1/4/c*ln(c*x^4+b*x^2+a)*A-1/4/c^2*ln(c*x^4+b*x^2+a)*b*B-1/c/(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/(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^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*B","A"
104,1,98,63,0.003000," ","int(x*(B*x^2+A)/(c*x^4+b*x^2+a),x)","\frac{A \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}-\frac{B 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{B \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c}"," ",0,"1/4*B*ln(c*x^4+b*x^2+a)/c+1/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A-1/2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*B*b/c","A"
105,1,105,70,0.007000," ","int((B*x^2+A)/x/(c*x^4+b*x^2+a),x)","-\frac{A 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{B \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}+\frac{A \ln \left(x \right)}{a}-\frac{A \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a}"," ",0,"A*ln(x)/a-1/4*A*ln(c*x^4+b*x^2+a)/a-1/2/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*b+1/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*B","A"
106,1,191,102,0.010000," ","int((B*x^2+A)/x^3/(c*x^4+b*x^2+a),x)","-\frac{A c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a}+\frac{A \,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 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{A b \ln \left(x \right)}{a^{2}}+\frac{A b \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a^{2}}+\frac{B \ln \left(x \right)}{a}-\frac{B \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a}-\frac{A}{2 a \,x^{2}}"," ",0,"-1/2*A/a/x^2-1/a^2*ln(x)*A*b+1/a*ln(x)*B+1/4/a^2*ln(c*x^4+b*x^2+a)*A*b-1/4/a*ln(c*x^4+b*x^2+a)*B-1/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*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))*A*b^2-1/2/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*B","A"
107,1,825,224,0.053000," ","int(x^4*(B*x^2+A)/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, A 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 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}\, A \,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}\, A \,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{3 \sqrt{2}\, B 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}\, B 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 \,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 \,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{B \,x^{3}}{3 c}+\frac{\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{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\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{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, B 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}\, B 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 \,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 \,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{A x}{c}-\frac{B b x}{c^{2}}"," ",0,"1/3*B*x^3/c+1/c*A*x-1/c^2*b*B*x+1/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*A*b+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*a*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(c*x*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*A*b^2+1/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*a*B-1/2/c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^2*B-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(c*x*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*a*b*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(c*x*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^3*B-1/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*A*b+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*a*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(c*x*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*A*b^2-1/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*a*B+1/2/c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^2*B-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(c*x*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*a*b*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(c*x*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^3*B","B"
108,1,560,171,0.026000," ","int(x^2*(B*x^2+A)/(c*x^4+b*x^2+a),x)","\frac{\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}}+\frac{\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}}+\frac{\sqrt{2}\, B 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}\, B 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 \,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 \,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}\, 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}}+\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}}+\frac{\sqrt{2}\, B 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 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{B x}{c}"," ",0,"B*x/c-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/(-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^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*B+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*B-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*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)*A+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)*A*b-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*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*B-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","B"
109,1,328,138,0.020000," ","int((B*x^2+A)/(c*x^4+b*x^2+a),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)}{\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)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, B 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 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}\, 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}}+\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}}"," ",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)*A-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/(-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*B-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+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)^(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*B","B"
110,1,353,153,0.030000," ","int((B*x^2+A)/x^2/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, A 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}\, A 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}\, B 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}\, B 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}}+\frac{\sqrt{2}\, A 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}\, A 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{A}{a x}"," ",0,"-A/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)*A+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)*A*b-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)*A+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)*A*b-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","B"
111,1,611,226,0.033000," ","int((B*x^2+A)/x^4/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, A \,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}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, A \,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}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, A \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, A \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, B 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 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}\, A b 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^{2}}+\frac{\sqrt{2}\, A b 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^{2}}+\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{\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{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{A b}{a^{2} x}-\frac{B}{a x}-\frac{A}{3 a \,x^{3}}"," ",0,"-1/3*A/a/x^3+1/a^2/x*A*b-1/a/x*B-1/2/a^2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b+1/a*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A-1/2/a^2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+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)*B+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*B+1/2/a^2*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b+1/a*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A-1/2/a^2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2-1/2/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)*B+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*B","B"
112,1,689,200,0.020000," ","int(x^7*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x)","\frac{3 A a b \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{A \,b^{3} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{B \,a^{2} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{2 B 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 \,b^{4} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{3 A 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{A \,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{6 B \,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 B 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 \,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{A \,a^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{A a \,b^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{A a \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) c}-\frac{A \,b^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) c^{2}}-\frac{3 B \,a^{2} b}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{B a \,b^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{2 B a b \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) c^{2}}+\frac{B \,b^{3} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(4 a c -b^{2}\right) c^{3}}+\frac{B \,x^{2}}{2 c^{2}}"," ",0,"1/2*B*x^2/c^2+3/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a*A*b-1/2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*A*b^3+1/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a^2*B-2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*a*b^2*B+1/2/c^3/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^2*b^4*B+1/c/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*A-1/2/c^2/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*A*b^2-3/2/c^2/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*b*B+1/2/c^3/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*b^3*B+1/c/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*a*A-1/4/c^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*A*b^2-2/c^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*a*b*B+1/2/c^3/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^3*B-3/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*a*b-6/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^2*B+6/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*B*a*b^2+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-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","B"
113,1,286,137,0.014000," ","int(x^5*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x)","\frac{2 A 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{3 B 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 \,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{B a \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) c}-\frac{B \,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(2 a A \,c^{2}-A \,b^{2} c -3 a b B c +b^{3} B \right) x^{2}}{\left(4 a c -b^{2}\right) c^{2}}+\frac{\left(A b c +2 a B c -b^{2} B \right) a}{\left(4 a c -b^{2}\right) c^{2}}}{2 c \,x^{4}+2 b \,x^{2}+2 a}"," ",0,"1/2*(-1/c^2*(2*A*a*c^2-A*b^2*c-3*B*a*b*c+B*b^3)/(4*a*c-b^2)*x^2+a*(A*b*c+2*B*a*c-B*b^2)/c^2/(4*a*c-b^2))/(c*x^4+b*x^2+a)+1/(4*a*c-b^2)/c*ln(c*x^4+b*x^2+a)*a*B-1/4/(4*a*c-b^2)/c^2*ln(c*x^4+b*x^2+a)*b^2*B+2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*A-3/(4*a*c-b^2)^(3/2)/c*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b*B+1/2/(4*a*c-b^2)^(3/2)/c^2*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*B","B"
114,1,158,103,0.012000," ","int(x^3*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x)","-\frac{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}}}+\frac{2 B 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{\left(A b c +2 a B c -b^{2} B \right) x^{2}}{\left(4 a c -b^{2}\right) c}-\frac{\left(2 A c -b B \right) a}{\left(4 a c -b^{2}\right) c}}{2 c \,x^{4}+2 b \,x^{2}+2 a}"," ",0,"1/2*(-(A*b*c+2*B*a*c-B*b^2)/c/(4*a*c-b^2)*x^2-a*(2*A*c-B*b)/(4*a*c-b^2)/c)/(c*x^4+b*x^2+a)-1/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*b+2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*B","A"
115,1,127,88,0.007000," ","int(x*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x)","\frac{2 A 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{B 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{A b -2 B a +\left(2 A c -b B \right) x^{2}}{2 \left(4 a c -b^{2}\right) \left(c \,x^{4}+b \,x^{2}+a \right)}"," ",0,"1/2*((2*A*c-B*b)*x^2+A*b-2*a*B)/(4*a*c-b^2)/(c*x^4+b*x^2+a)+2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*c-1/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*B","A"
116,1,361,139,0.018000," ","int((B*x^2+A)/x/(c*x^4+b*x^2+a)^2,x)","-\frac{A b c \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{B c \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{3 A 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{A \,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{2 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}}}-\frac{A \,b^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{A c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a}+\frac{A \,b^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) a^{2}}+\frac{A c}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{B b}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{A \ln \left(x \right)}{a^{2}}"," ",0,"A*ln(x)/a^2-1/2/a/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*A*b+1/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*B+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A*c-1/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A*b^2+1/2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b*B-1/a/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)*A+1/4/a^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*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))*A*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))*A*b^3+2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*B*c","B"
117,1,622,209,0.023000," ","int((B*x^2+A)/x^3/(c*x^4+b*x^2+a)^2,x)","-\frac{A \,c^{2} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{A \,b^{2} c \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{B b c \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{6 A \,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 A \,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{A \,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 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 \,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{3 A b c}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{A \,b^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{2 A b c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a^{2}}-\frac{A \,b^{3} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(4 a c -b^{2}\right) a^{3}}-\frac{B \,b^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{B c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a}+\frac{B \,b^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) a^{2}}+\frac{B c}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{2 A b \ln \left(x \right)}{a^{3}}+\frac{B \ln \left(x \right)}{a^{2}}-\frac{A}{2 a^{2} x^{2}}"," ",0,"-1/2*A/a^2/x^2-2/a^3*ln(x)*A*b+1/a^2*ln(x)*B-1/a/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^2*A+1/2/a^2/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*A*b^2-1/2/a/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*b*B-3/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A*b*c+1/2/a^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*A*b^3+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*B*c-1/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*B*b^2+2/a^2/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)*A*b-1/2/a^3/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*A*b^3-1/a/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)*B+1/4/a^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^2*B-6/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*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))*A*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))*A*b^4-3/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*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*b^3","B"
118,1,1507,377,0.043000," ","int(x^6*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x)","-\frac{A a \,x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{A \,b^{2} x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}+\frac{3 B a b \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{B \,b^{3} x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{2 \sqrt{2}\, A a b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, A a b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, A \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{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{5 \sqrt{2}\, B \,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}\, B \,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}\, B 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}\, B 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 \,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 \,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 a b x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{3 \sqrt{2}\, A 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 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}\, 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{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, A \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{B \,a^{2} x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{B 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}\, B 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}\, B 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 \,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 \,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{B x}{c^{2}}"," ",0,"1/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*A*b^2+1/c/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*x*B-1/2/c^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*b^3*B-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*A+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*A-1/2/c^2/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*b^2*B+3/2/c/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a*b*B+1/2/c/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*A*b+1/4/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2-3/4/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*B-1/4/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+3/4/c^2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*B+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*B+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*B-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*B-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*B-1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x^3*a*A+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*A*b+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*A*b+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-1/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^3+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*B+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*B-1/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^3-13/4/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*B+B/c^2*x","B"
119,1,1030,293,0.036000," ","int(x^4*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x)","-\frac{\sqrt{2}\, A a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{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}\, 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}}+\frac{2 \sqrt{2}\, B a b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, B a b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, B \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, B \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{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}\, 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}}-\frac{\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}}-\frac{3 \sqrt{2}\, B 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}\, B 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 \,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 \,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{\left(A b c +2 a B c -b^{2} B \right) x^{3}}{2 \left(4 a c -b^{2}\right) c}-\frac{\left(2 A c -b B \right) a x}{2 \left(4 a c -b^{2}\right) c}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2*(A*b*c+2*B*a*c-B*b^2)/c/(4*a*c-b^2)*x^3-1/2*(2*A*c-B*b)/(4*a*c-b^2)*a/c*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)*A*b-1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*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)*A*b^2-3/2/(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*B+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*B+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*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*B-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)*A*b-1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*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)*A*b^2+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*B-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*B+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*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","B"
120,1,733,234,0.029000," ","int(x^2*(B*x^2+A)/(c*x^4+b*x^2+a)^2,x)","\frac{\sqrt{2}\, A b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, A b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, B a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, B a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, B \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{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 \,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}\, A 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}\, A 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{\sqrt{2}\, B 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 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{\left(2 A c -b B \right) x^{3}}{8 a c -2 b^{2}}+\frac{\left(A b -2 B a \right) x}{8 a c -2 b^{2}}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(1/2*(2*A*c-B*b)/(4*a*c-b^2)*x^3+1/2*(A*b-2*B*a)/(4*a*c-b^2)*x)/(c*x^4+b*x^2+a)-1/2/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A+1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b+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*B-1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*B-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*B+1/2/(4*a*c-b^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A+1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b-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*B-1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*B-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","B"
121,1,1761,251,0.110000," ","int((B*x^2+A)/(c*x^4+b*x^2+a)^2,x)","-\frac{12 \sqrt{2}\, A a \,c^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{12 \sqrt{2}\, A a \,c^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, A \,b^{4} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{3 \sqrt{2}\, A \,b^{4} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{8 \sqrt{2}\, A \,b^{2} c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{8 \sqrt{2}\, A \,b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{4 \sqrt{2}\, B a b \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{4 \sqrt{2}\, B a b \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, B \,b^{3} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, B \,b^{3} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, A \,b^{3} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \sqrt{2}\, A \,b^{3} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, A b \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A b \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{2 \sqrt{2}\, B a \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, B a \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, B \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, B \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \left(4 a c +3 b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{A 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{A 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}{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}{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{\sqrt{-4 a c +b^{2}}\, A 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{\sqrt{-4 a c +b^{2}}\, A 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)*(-4*a*c+b^2)^(1/2)/a*x/(x^2+1/2*(-4*a*c+b^2)^(1/2)/c+1/2*b/c)*A-1/4/(4*a*c-b^2)/a*x/(x^2+1/2*(-4*a*c+b^2)^(1/2)/c+1/2*b/c)*A*b+1/2/(4*a*c-b^2)*x/(x^2+1/2*(-4*a*c+b^2)^(1/2)/c+1/2*b/c)*B-12*c^3/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*a-8*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+3/4*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)/a/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^4-c^2/(4*a*c-b^2)/(4*a*c+3*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/(4*a*c-b^2)/a/(4*a*c+3*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+2*c^2/(4*a*c-b^2)*a/(4*a*c+3*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+3/2*c/(4*a*c-b^2)/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*b^2+4*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*a/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*B+3*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)/(4*a*c+3*b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*b^3-1/4/(4*a*c-b^2)*(-4*a*c+b^2)^(1/2)/a*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*A-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)*A*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)*B-12*c^3/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*a-8*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^2+3/4*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)/a/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^4+c^2/(4*a*c-b^2)/(4*a*c+3*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/(4*a*c-b^2)/a/(4*a*c+3*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^3-2*c^2/(4*a*c-b^2)*a/(4*a*c+3*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-3/2*c/(4*a*c-b^2)/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*b^2+4*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*a/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*B+3*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)/(4*a*c+3*b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*b^3","B"
122,1,1252,337,0.040000," ","int((B*x^2+A)/x^2/(c*x^4+b*x^2+a)^2,x)","-\frac{A \,c^{2} x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{A \,b^{2} c \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{B b c \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{4 \sqrt{2}\, A b \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, A b \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \sqrt{2}\, A \,b^{3} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, A \,b^{3} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, B \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, B \,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{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \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}}-\frac{3 \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}}-\frac{3 A b c x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{5 \sqrt{2}\, A \,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}\, A \,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{A \,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}\, A \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{3 \sqrt{2}\, A \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{B \,b^{2} x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{\sqrt{2}\, B 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 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{B c x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{A}{a^{2} x}"," ",0,"-A/a^2/x-1/a/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^3*A+1/2/a^2/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*A*b^2-1/2/a/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*b*B-3/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*A*b*c+1/2/a^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*A*b^3+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*B*c-1/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*B*b^2+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)*A-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)*A*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)*A*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)*A*b^3+1/4/a*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*B-3*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B+1/4/a*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*b^2-5/2/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)*A+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)*A*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)*A*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)*A*b^3-1/4/a*c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*B-3*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B+1/4/a*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B*b^2","B"
123,1,1653,459,0.047000," ","int((B*x^2+A)/x^4/(c*x^4+b*x^2+a)^2,x)","\frac{3 A 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{A \,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{B \,c^{2} x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{B \,b^{2} c \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{7 \sqrt{2}\, A \,c^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{7 \sqrt{2}\, A \,c^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{29 \sqrt{2}\, A \,b^{2} c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{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}\, A \,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}\, A \,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}\, A \,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{4 \sqrt{2}\, B b \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, B b \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \sqrt{2}\, B \,b^{3} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{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 \,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{A \,c^{2} x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{2 A \,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}\, A 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}\, A 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{A \,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}\, A \,b^{3} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}-\frac{5 \sqrt{2}\, A \,b^{3} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}-\frac{3 B b c x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{5 \sqrt{2}\, B \,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}\, B \,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 \,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 \,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 \,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{2 A b}{a^{3} x}-\frac{B}{a^{2} x}-\frac{A}{3 a^{2} x^{3}}"," ",0,"1/2/a^2/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*B*b^2+2/a^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*A*b^2*c-3/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*b*B*c+3/2/a^2/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^3*A*b-1/2/a^3/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*A*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)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*B-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)*B+2/a^3/x*A*b+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)*A-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*b^2+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)*A*b+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)*A+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*b^2+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)*A*b^3-5/4/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)*A*b^3-19/4/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)*A*b-1/3*A/a^2/x^3-1/a^2/x*B-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)*A*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*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*b^3+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)*A*b^4+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)*A*b^4-29/4/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)*A*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*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*b^3-1/a/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^3*B-1/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*A*c^2+1/2/a^2/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*B*b^3-1/2/a^3/(c*x^4+b*x^2+a)/(4*a*c-b^2)*x*A*b^4","B"
124,1,2054,351,0.031000," ","int(x^11*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x)","\frac{25 A \,a^{2} b \,x^{6}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{15 A a \,b^{3} x^{6}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}+\frac{A \,b^{5} x^{6}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{9 B \,a^{3} x^{6}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{51 B \,a^{2} b^{2} x^{6}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}+\frac{12 B a \,b^{4} x^{6}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}-\frac{3 B \,b^{6} x^{6}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{8 A \,a^{3} x^{4}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{11 A \,a^{2} b^{2} x^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{19 A a \,b^{4} x^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{3 A \,b^{6} x^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{21 B \,a^{3} b \,x^{4}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{41 B \,a^{2} b^{3} x^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{17 B a \,b^{5} x^{4}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{5 B \,b^{7} x^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{31 A \,a^{3} b \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{11 A \,a^{2} b^{3} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{3 A a \,b^{5} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{7 B \,a^{4} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{71 B \,a^{3} b^{2} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{19 B \,a^{2} b^{4} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{5 B a \,b^{6} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{6 A \,a^{4}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{21 A \,a^{3} b^{2}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{3 A \,a^{2} b^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{15 A \,a^{2} b \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c}+\frac{5 A a \,b^{3} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{A \,b^{5} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{3}}-\frac{29 B \,a^{4} b}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{9 B \,a^{3} b^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{30 B \,a^{3} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c}-\frac{5 B \,a^{2} b^{5}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{45 B \,a^{2} b^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{15 B a \,b^{4} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{3}}+\frac{3 B \,b^{6} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{4}}+\frac{4 A \,a^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{2 A a \,b^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{A \,b^{4} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{12 B \,a^{2} b \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{6 B a \,b^{3} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{3 B \,b^{5} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{B \,x^{2}}{2 c^{3}}"," ",0,"1/2*B*x^2/c^3+6/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*B*a*b^3-1/2/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^5*A-2/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*A*a*b^2-12/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*B*a^2*b+1/c^2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*A*b^5-5/4/c^4/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*B*b^7+7/c/(c*x^4+b*x^2+a)^2*a^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*B-21/4/c^2/(c*x^4+b*x^2+a)^2*a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*A*b^2-29/2/c^2/(c*x^4+b*x^2+a)^2*a^4/(16*a^2*c^2-8*a*b^2*c+b^4)*B*b-5/4/c^4/(c*x^4+b*x^2+a)^2*a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*B*b^5+25/2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*A*a^2*b+3/2/c^4/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^6*B-30/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^3*B-3/2/c^3/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*B*b^6+3/4/c^3/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*A*b^6+3/4/c^3/(c*x^4+b*x^2+a)^2*a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*A*b^4+9/c^3/(c*x^4+b*x^2+a)^2*a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*B*b^3+3/2/c^3/(c*x^4+b*x^2+a)^2*a/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*A*b^5-11/c^2/(c*x^4+b*x^2+a)^2*a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*A*b^3+11/4/c/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*A*a^2*b^2-19/4/c^2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*A*a*b^4-21/2/c/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*B*a^3*b-41/4/c^2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*B*a^2*b^3+31/2/c/(c*x^4+b*x^2+a)^2*a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*A*b-71/2/c^2/(c*x^4+b*x^2+a)^2*a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*B*b^2-5/2/c^4/(c*x^4+b*x^2+a)^2*a/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*B*b^6-15/2/c/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*A*a*b^3+12/c^2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*B*a*b^4-15/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*a^2*b+5/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*a*b^3+45/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*B*a^2*b^2-15/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*B*a*b^4+19/c^3/(c*x^4+b*x^2+a)^2*a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*B*b^4+17/2/c^3/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*B*a*b^5-51/2/c/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*B*a^2*b^2+9/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*B*a^3+8/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*A*a^3+6/c/(c*x^4+b*x^2+a)^2*a^4/(16*a^2*c^2-8*a*b^2*c+b^4)*A+1/4/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*A*b^4+4/c/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*A*a^2-3/4/c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*B*b^5","B"
125,1,723,242,0.026000," ","int(x^9*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x)","\frac{6 A \,a^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}-\frac{15 B \,a^{2} b \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c}+\frac{5 B a \,b^{3} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{B \,b^{5} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{3}}+\frac{4 B \,a^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{2 B a \,b^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{B \,b^{4} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{-\frac{\left(10 A \,a^{2} c^{3}-8 A a \,b^{2} c^{2}+A \,b^{4} c -25 B \,a^{2} b \,c^{2}+15 B a \,b^{3} c -2 B \,b^{5}\right) x^{6}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{\left(2 A \,a^{2} b \,c^{3}+8 A a \,b^{3} c^{2}-A \,b^{5} c +32 B \,a^{3} c^{3}+11 B \,a^{2} b^{2} c^{2}-19 B a \,b^{4} c +3 B \,b^{6}\right) x^{4}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{\left(6 A \,a^{2} c^{3}-10 A a \,b^{2} c^{2}+A \,b^{4} c -31 B \,a^{2} b \,c^{2}+22 B a \,b^{3} c -3 B \,b^{5}\right) a \,x^{2}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{\left(10 a A b \,c^{2}-A \,b^{3} c +24 a^{2} B \,c^{2}-21 a \,b^{2} B c +3 b^{4} B \right) a^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"1/2*(-1/c^2*(10*A*a^2*c^3-8*A*a*b^2*c^2+A*b^4*c-25*B*a^2*b*c^2+15*B*a*b^3*c-2*B*b^5)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+1/2*(2*A*a^2*b*c^3+8*A*a*b^3*c^2-A*b^5*c+32*B*a^3*c^3+11*B*a^2*b^2*c^2-19*B*a*b^4*c+3*B*b^6)/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4-a*(6*A*a^2*c^3-10*A*a*b^2*c^2+A*b^4*c-31*B*a^2*b*c^2+22*B*a*b^3*c-3*B*b^5)/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2+1/2*a^2*(10*A*a*b*c^2-A*b^3*c+24*B*a^2*c^2-21*B*a*b^2*c+3*B*b^4)/c^3/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^4+b*x^2+a)^2+4/c/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*a^2*B-2/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*a*b^2*B+1/4/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*b^4*B+6/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*a^2-15/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^2*b*B+5/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*B*a*b^3-1/2/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^5*B","B"
126,1,398,138,0.017000," ","int(x^7*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x)","-\frac{3 A a b \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{6 B \,a^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{-\frac{\left(3 a A b \,c^{2}+10 a^{2} B \,c^{2}-8 a \,b^{2} B c +b^{4} B \right) x^{6}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{\left(16 A \,a^{2} c^{3}+A a \,b^{2} c^{2}+A \,b^{4} c -2 B \,a^{2} b \,c^{2}-8 B a \,b^{3} c +B \,b^{5}\right) x^{4}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}-\frac{\left(5 a A b \,c^{2}+A \,b^{3} c +6 a^{2} B \,c^{2}-10 a \,b^{2} B c +b^{4} B \right) a \,x^{2}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}-\frac{\left(8 a A \,c^{2}+A \,b^{2} c -10 a b B c +b^{3} B \right) a^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"1/2*(-(3*A*a*b*c^2+10*B*a^2*c^2-8*B*a*b^2*c+B*b^4)/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6-1/2*(16*A*a^2*c^3+A*a*b^2*c^2+A*b^4*c-2*B*a^2*b*c^2-8*B*a*b^3*c+B*b^5)/(16*a^2*c^2-8*a*b^2*c+b^4)/c^2*x^4-a*(5*A*a*b*c^2+A*b^3*c+6*B*a^2*c^2-10*B*a*b^2*c+B*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/c^2*x^2-1/2*a^2/c^2*(8*A*a*c^2+A*b^2*c-10*B*a*b*c+B*b^3)/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^4+b*x^2+a)^2-3*a/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*b+6*a^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*B","B"
127,1,411,179,0.020000," ","int(x^5*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x)","\frac{2 A a c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{A \,b^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}-\frac{3 B a b \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{\frac{\left(2 a A c +A \,b^{2}-3 a b B \right) c \,x^{6}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}+\frac{\left(6 a A b \,c^{2}+3 A \,b^{3} c -16 a^{2} B \,c^{2}-a \,b^{2} B c -b^{4} B \right) x^{4}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{\left(2 a A \,c^{2}-5 A \,b^{2} c +5 a b B c +b^{3} B \right) a \,x^{2}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}+\frac{\left(6 A b c -8 a B c -b^{2} B \right) a^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"1/2*(c*(2*A*a*c+A*b^2-3*B*a*b)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+1/2*(6*A*a*b*c^2+3*A*b^3*c-16*B*a^2*c^2-B*a*b^2*c-B*b^4)/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4-a/c*(2*A*a*c^2-5*A*b^2*c+5*B*a*b*c+B*b^3)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2+1/2*a^2*(6*A*b*c-8*B*a*c-B*b^2)/c/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^4+b*x^2+a)^2+2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*A*c+1/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*b^2-3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b*B","B"
128,1,379,164,0.017000," ","int(x^3*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x)","-\frac{3 A b c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{2 B a c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{B \,b^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{-\frac{\left(3 A b c -2 a B c -b^{2} B \right) c \,x^{6}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}-\frac{3 \left(3 A b c -2 a B c -b^{2} B \right) b \,x^{4}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(5 A a b c +A \,b^{3}+2 a^{2} B c -5 B a \,b^{2}\right) x^{2}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}-\frac{\left(8 a A c +A \,b^{2}-6 a b B \right) a}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"1/2*(-c*(3*A*b*c-2*B*a*c-B*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6-3/2*b*(3*A*b*c-2*B*a*c-B*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4-(5*A*a*b*c+A*b^3+2*B*a^2*c-5*B*a*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-1/2*a*(8*A*a*c+A*b^2-6*B*a*b)/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^4+b*x^2+a)^2-3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*b*c+2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*B*c+1/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*B","B"
129,1,262,131,0.010000," ","int(x*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x)","\frac{3 A \,c^{2} x^{2}}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{4}+b \,x^{2}+a \right)}-\frac{3 B b c \,x^{2}}{2 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{4}+b \,x^{2}+a \right)}+\frac{6 A \,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{5}{2}}}-\frac{3 B 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{5}{2}}}+\frac{3 A b c}{2 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{4}+b \,x^{2}+a \right)}-\frac{3 B \,b^{2}}{4 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{4}+b \,x^{2}+a \right)}+\frac{A b -2 B a +\left(2 A c -b B \right) x^{2}}{4 \left(4 a c -b^{2}\right) \left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"1/4*(A*b-2*B*a+(2*A*c-B*b)*x^2)/(4*a*c-b^2)/(c*x^4+b*x^2+a)^2+3/(4*a*c-b^2)^2/(c*x^4+b*x^2+a)*c^2*x^2*A-3/2/(4*a*c-b^2)^2/(c*x^4+b*x^2+a)*c*x^2*b*B+3/2/(4*a*c-b^2)^2/(c*x^4+b*x^2+a)*b*A*c-3/4/(4*a*c-b^2)^2/(c*x^4+b*x^2+a)*b^2*B+6/(4*a*c-b^2)^(5/2)*c^2*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A-3/(4*a*c-b^2)^(5/2)*c*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*B","A"
130,1,1161,239,0.029000," ","int((B*x^2+A)/x/(c*x^4+b*x^2+a)^3,x)","-\frac{7 A b \,c^{3} x^{6}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{A \,b^{3} c^{2} x^{6}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{3 B \,c^{3} x^{6}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{29 A \,b^{2} c^{2} x^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{A \,b^{4} c \,x^{4}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{4 A \,c^{3} x^{4}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{9 B b \,c^{2} x^{4}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{3 A \,b^{3} c \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{A \,b^{5} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{A b \,c^{2} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{5 B a \,c^{2} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{B \,b^{2} c \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{6 A a \,c^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{3 A \,b^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}-\frac{15 A b \,c^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a}+\frac{5 A \,b^{3} c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{2}}-\frac{A \,b^{5} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{3}}-\frac{21 A \,b^{2} c}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{5 B a b c}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{B \,b^{3}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{6 B \,c^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}-\frac{4 A \,c^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{2 A \,b^{2} c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{A \,b^{4} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}+\frac{A \ln \left(x \right)}{a^{3}}"," ",0,"9/2/(c*x^4+b*x^2+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b*B-1/2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*A*b*c^2+1/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*B*b^2*c+1/2/a^2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*A*b^5+5*a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*B*c^2+5/2*a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b*B*c+2/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c*ln(c*x^4+b*x^2+a)*A*b^2-1/2/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*b^5+A*ln(x)/a^3-1/4/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*B*b^3-7/2/a/(c*x^4+b*x^2+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*A*b+1/2/a^2/(c*x^4+b*x^2+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*A*b^3-29/4/a/(c*x^4+b*x^2+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*A*b^2+1/a^2/(c*x^4+b*x^2+a)^2*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*A*b^4-3/a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*A*b^3*c-15/a/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*b*c^2+5/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*b^3*c-21/4/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*A*b^2*c+6*a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*A*c^2+3/4/a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*A*b^4-4/a/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*ln(c*x^4+b*x^2+a)*A-1/4/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*A*b^4+6/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*B*c^2+3/(c*x^4+b*x^2+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*B+4/(c*x^4+b*x^2+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*A","B"
131,1,1862,349,0.039000," ","int((B*x^2+A)/x^3/(c*x^4+b*x^2+a)^3,x)","-\frac{7 A \,c^{4} x^{6}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{13 A \,b^{2} c^{3} x^{6}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{A \,b^{4} c^{2} x^{6}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{7 B b \,c^{3} x^{6}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{B \,b^{3} c^{2} x^{6}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{37 A b \,c^{3} x^{4}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{55 A \,b^{3} c^{2} x^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{2 A \,b^{5} c \,x^{4}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{29 B \,b^{2} c^{2} x^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{B \,b^{4} c \,x^{4}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{4 B \,c^{3} x^{4}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{7 A \,b^{2} c^{2} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{6 A \,b^{4} c \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{A \,b^{6} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{9 A \,c^{3} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{3 B \,b^{3} c \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{B \,b^{5} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{B b \,c^{2} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{9 A \,b^{3} c}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}-\frac{30 A \,c^{3} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a}-\frac{5 A \,b^{5}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{45 A \,b^{2} c^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{2}}-\frac{15 A \,b^{4} c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{3}}+\frac{3 A \,b^{6} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{4}}-\frac{29 A b \,c^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{6 B a \,c^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{3 B \,b^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}-\frac{15 B b \,c^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a}+\frac{5 B \,b^{3} c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{2}}-\frac{B \,b^{5} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{3}}-\frac{21 B \,b^{2} c}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{12 A b \,c^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{6 A \,b^{3} c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}+\frac{3 A \,b^{5} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{4}}-\frac{4 B \,c^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{2 B \,b^{2} c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{B \,b^{4} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{3 A b \ln \left(x \right)}{a^{4}}+\frac{B \ln \left(x \right)}{a^{3}}-\frac{A}{2 a^{3} x^{2}}"," ",0,"6/a^2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*A*b^4*c-3/a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*B*b^3*c+13/2/a^2/(c*x^4+b*x^2+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*A*b^2-1/a^3/(c*x^4+b*x^2+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*A*b^4-7/2/a/(c*x^4+b*x^2+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*b*B+1/2/a^2/(c*x^4+b*x^2+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*B*b^3-37/2/a/(c*x^4+b*x^2+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*A*b+55/4/a^2/(c*x^4+b*x^2+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*A*b^3+45/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*b^2*c^2-15/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*b^4*c-15/a/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*B*b*c^2+5/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*B*b^3*c-2/a^3/(c*x^4+b*x^2+a)^2*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*A*b^5-29/4/a/(c*x^4+b*x^2+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*B*b^2+1/a^2/(c*x^4+b*x^2+a)^2*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*B*b^4-7/2/a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*A*b^2*c^2-3/a^4*ln(x)*A*b+3/4/a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*B*b^4+3/4/a^4/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*A*b^5-4/a/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*ln(c*x^4+b*x^2+a)*B-1/4/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*B*b^4+4/(c*x^4+b*x^2+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*B-9/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*A*c^3-29/2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*A*b*c^2-21/4/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*B*b^2*c-1/2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*B*b*c^2-7/a/(c*x^4+b*x^2+a)^2*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*A-1/a^3/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*A*b^6+1/2/a^2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*B*b^5+9/a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*A*b^3*c+12/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*ln(c*x^4+b*x^2+a)*A*b-6/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c*ln(c*x^4+b*x^2+a)*A*b^3+2/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c*ln(c*x^4+b*x^2+a)*B*b^2-30/a/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*c^3-1/2/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*B*b^5+3/2/a^4/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*A*b^6-5/4/a^2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*A*b^5+6*a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*B*c^2-1/2*A/a^3/x^2+1/a^3*ln(x)*B","B"
132,1,2015,506,0.069000," ","int(x^8*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x)","-\frac{5 \sqrt{2}\, A \,a^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{5 \sqrt{2}\, A \,a^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{9 \sqrt{2}\, A a \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{9 \sqrt{2}\, A a \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, A \,b^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, A \,b^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{33 \sqrt{2}\, B \,a^{2} b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{33 \sqrt{2}\, B \,a^{2} b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{33 \sqrt{2}\, B a \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{33 \sqrt{2}\, B a \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{3 \sqrt{2}\, B \,b^{5} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\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 \,b^{5} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, A a b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A a b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, A \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{21 \sqrt{2}\, B \,a^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{21 \sqrt{2}\, B \,a^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{27 \sqrt{2}\, B a \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{27 \sqrt{2}\, B a \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, B \,b^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, B \,b^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{-\frac{\left(16 a A b \,c^{2}-A \,b^{3} c +44 a^{2} B \,c^{2}-37 a \,b^{2} B c +5 b^{4} B \right) x^{7}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{\left(36 A \,a^{2} c^{3}+5 A a \,b^{2} c^{2}+A \,b^{4} c -4 B \,a^{2} b \,c^{2}-20 B a \,b^{3} c +3 B \,b^{5}\right) x^{5}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}-\frac{\left(28 a A b \,c^{2}+2 A \,b^{3} c +28 a^{2} B \,c^{2}-49 a \,b^{2} B c +6 b^{4} B \right) a \,x^{3}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}-\frac{\left(20 a A \,c^{2}+A \,b^{2} c -24 a b B c +3 b^{3} B \right) a^{2} x}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"(-1/8*(16*A*a*b*c^2-A*b^3*c+44*B*a^2*c^2-37*B*a*b^2*c+5*B*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/c*x^7-1/8*(36*A*a^2*c^3+5*A*a*b^2*c^2+A*b^4*c-4*B*a^2*b*c^2-20*B*a*b^3*c+3*B*b^5)/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5-1/8*a/c^2*(28*A*a*b*c^2+2*A*b^3*c+28*B*a^2*c^2-49*B*a*b^2*c+6*B*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3-1/8*a^2*(20*A*a*c^2+A*b^2*c-24*B*a*b*c+3*B*b^3)/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x)/(c*x^4+b*x^2+a)^2+1/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A*b-1/16/c/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b+(-4*a*c+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^3-5/2*c/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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*a^2-9/8/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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*a*b^2+1/16/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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^4-21/4/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*B+27/16/c/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b+(-4*a*c+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*B-3/16/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b+(-4*a*c+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*B+33/4/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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^2*b-33/16/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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*b^3+3/16/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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*b^5-1/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A*b+1/16/c/(16*a^2*c^2-8*a*b^2*c+b^4)*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^3-5/2*c/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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*a^2-9/8/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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*a*b^2+1/16/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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^4+21/4/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*B-27/16/c/(16*a^2*c^2-8*a*b^2*c+b^4)*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*B+3/16/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*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+33/4/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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^2*b-33/16/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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*b^3+3/16/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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*b^5","B"
133,1,1631,415,0.048000," ","int(x^6*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x)","\frac{9 \sqrt{2}\, A a b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{9 \sqrt{2}\, A a b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, A \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, A \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{5 \sqrt{2}\, B \,a^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{5 \sqrt{2}\, B \,a^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{9 \sqrt{2}\, B a \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{9 \sqrt{2}\, B a \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, B \,b^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, B \,b^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, A a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, A a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, A \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, A \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, B a b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, B a b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, B \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, B \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\frac{\left(12 a A \,c^{2}+3 A \,b^{2} c -16 a b B c +b^{3} B \right) x^{7}}{128 a^{2} c^{2}-64 a \,b^{2} c +8 b^{4}}+\frac{\left(16 a A b \,c^{2}+5 A \,b^{3} c -36 a^{2} B \,c^{2}-5 a \,b^{2} B c -b^{4} B \right) x^{5}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{\left(4 a A \,c^{2}-19 A \,b^{2} c +28 a b B c +2 b^{3} B \right) a \,x^{3}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}+\frac{\left(12 A b c -20 a B c -b^{2} B \right) a^{2} x}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"(1/8*(12*A*a*c^2+3*A*b^2*c-16*B*a*b*c+B*b^3)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^7+1/8*(16*A*a*b*c^2+5*A*b^3*c-36*B*a^2*c^2-5*B*a*b^2*c-B*b^4)/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5-1/8*a/c*(4*A*a*c^2-19*A*b^2*c+28*B*a*b*c+2*B*b^3)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+1/8*a^2*(12*A*b*c-20*B*a*c-B*b^2)/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x)/(c*x^4+b*x^2+a)^2-3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A-3/16/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b+(-4*a*c+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+9/4/(16*a^2*c^2-8*a*b^2*c+b^4)*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*A*b+3/16/(16*a^2*c^2-8*a*b^2*c+b^4)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^3+1/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*B-1/16/(16*a^2*c^2-8*a*b^2*c+b^4)/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^3*B-5/2/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*B-9/8/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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*B+1/16/(16*a^2*c^2-8*a*b^2*c+b^4)/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^4*B+3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A+3/16/(16*a^2*c^2-8*a*b^2*c+b^4)*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+9/4/(16*a^2*c^2-8*a*b^2*c+b^4)*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*A*b+3/16/(16*a^2*c^2-8*a*b^2*c+b^4)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b^3-1/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*B+1/16/(16*a^2*c^2-8*a*b^2*c+b^4)/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^3*B-5/2/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*B-9/8/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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*B+1/16/(16*a^2*c^2-8*a*b^2*c+b^4)/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^4*B","B"
134,1,1283,336,0.049000," ","int(x^4*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x)","-\frac{3 \sqrt{2}\, A a \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, A a \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{9 \sqrt{2}\, A \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{9 \sqrt{2}\, A \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{9 \sqrt{2}\, B a b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{9 \sqrt{2}\, B a b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, B \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, B \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, A b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, A b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, B a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, B a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, B \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, B \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{-\frac{3 \left(4 A b c -4 a B c -b^{2} B \right) c \,x^{7}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{\left(4 a A \,c^{2}-19 A \,b^{2} c +16 a b B c +5 b^{3} B \right) x^{5}}{128 a^{2} c^{2}-64 a \,b^{2} c +8 b^{4}}-\frac{\left(16 A a b c +5 A \,b^{3}+4 a^{2} B c -19 B a \,b^{2}\right) x^{3}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{3 \left(4 a A c +A \,b^{2}-4 a b B \right) a x}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"(-3/8*c*(4*A*b*c-4*B*a*c-B*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^7+1/8*(4*A*a*c^2-19*A*b^2*c+16*B*a*b*c+5*B*b^3)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5-1/8*(16*A*a*b*c+5*A*b^3+4*B*a^2*c-19*B*a*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3-3/8*a*(4*A*a*c+A*b^2-4*B*a*b)/(16*a^2*c^2-8*a*b^2*c+b^4)*x)/(c*x^4+b*x^2+a)^2+3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*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*b-3/2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A-9/8/(16*a^2*c^2-8*a*b^2*c+b^4)*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^2-3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*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*B-3/16/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b+(-4*a*c+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+9/4/(16*a^2*c^2-8*a*b^2*c+b^4)*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*B+3/16/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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*B-3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*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*b-3/2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*A-9/8/(16*a^2*c^2-8*a*b^2*c+b^4)*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^2+3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*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*B+3/16/(16*a^2*c^2-8*a*b^2*c+b^4)*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+9/4/(16*a^2*c^2-8*a*b^2*c+b^4)*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*B+3/16/(16*a^2*c^2-8*a*b^2*c+b^4)/(-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","B"
135,1,1335,382,0.046000," ","int(x^2*(B*x^2+A)/(c*x^4+b*x^2+a)^3,x)","-\frac{\sqrt{2}\, A \,b^{3} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, A \,b^{3} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{13 \sqrt{2}\, A b \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{13 \sqrt{2}\, A b \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, B a \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, B a \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{9 \sqrt{2}\, B \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{9 \sqrt{2}\, B \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, A \,b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, A \,b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{5 \sqrt{2}\, A \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{5 \sqrt{2}\, A \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, B b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, B b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\frac{\left(20 a A c +A \,b^{2}-12 a b B \right) c^{2} x^{7}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{\left(28 A a b c +2 A \,b^{3}+4 a^{2} B c -19 B a \,b^{2}\right) c \,x^{5}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{\left(36 A \,a^{2} c^{2}+5 A a \,b^{2} c +A \,b^{4}-16 a^{2} b B c -5 B a \,b^{3}\right) x^{3}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{\left(16 A a b c -A \,b^{3}-12 a^{2} B c -3 B a \,b^{2}\right) x}{128 a^{2} c^{2}-64 a \,b^{2} c +8 b^{4}}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"(1/8*c^2*(20*A*a*c+A*b^2-12*B*a*b)/a/(16*a^2*c^2-8*a*b^2*c+b^4)*x^7+1/8/a*c*(28*A*a*b*c+2*A*b^3+4*B*a^2*c-19*B*a*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5+1/8*(36*A*a^2*c^2+5*A*a*b^2*c+A*b^4-16*B*a^2*b*c-5*B*a*b^3)/a/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+1/8*(16*A*a*b*c-A*b^3-12*B*a^2*c-3*B*a*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x)/(c*x^4+b*x^2+a)^2-5/4/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A-1/16/a/(16*a^2*c^2-8*a*b^2*c+b^4)*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*b^2+13/4/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b-1/16/a/(16*a^2*c^2-8*a*b^2*c+b^4)*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^3+3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*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*B-3/2*a/(16*a^2*c^2-8*a*b^2*c+b^4)*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-9/8/(16*a^2*c^2-8*a*b^2*c+b^4)*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*b^2+5/4/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A+1/16/a/(16*a^2*c^2-8*a*b^2*c+b^4)*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*b^2+13/4/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*A*b-1/16/a/(16*a^2*c^2-8*a*b^2*c+b^4)*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^3-3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*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*B-3/2*a/(16*a^2*c^2-8*a*b^2*c+b^4)*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-9/8/(16*a^2*c^2-8*a*b^2*c+b^4)*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*b^2","B"
136,1,11936,416,0.281000," ","int((B*x^2+A)/(c*x^4+b*x^2+a)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
137,1,18,21,0.006000," ","int(x*(4*x^2-7)/(x^4-5*x^2+4),x)","\frac{3 \ln \left(x^{2}-4\right)}{2}+\frac{\ln \left(x^{2}-1\right)}{2}"," ",0,"3/2*ln(x^2-4)+1/2*ln(x^2-1)","A"
138,1,18,21,0.004000," ","int((4*x^3-7*x)/(x^4-5*x^2+4),x)","\frac{3 \ln \left(x^{2}-4\right)}{2}+\frac{\ln \left(x^{2}-1\right)}{2}"," ",0,"3/2*ln(x^2-4)+1/2*ln(x^2-1)","A"
139,1,31,30,0.003000," ","int(x*(x^2+2)/(x^4+x^2+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}+1\right) \sqrt{3}}{3}\right)}{2}+\frac{\ln \left(x^{4}+x^{2}+1\right)}{4}"," ",0,"1/4*ln(x^4+x^2+1)+1/2*arctan(1/3*(2*x^2+1)*3^(1/2))*3^(1/2)","A"
140,1,31,30,0.003000," ","int((x^3+2*x)/(x^4+x^2+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}+1\right) \sqrt{3}}{3}\right)}{2}+\frac{\ln \left(x^{4}+x^{2}+1\right)}{4}"," ",0,"1/2*3^(1/2)*arctan(1/3*(2*x^2+1)*3^(1/2))+1/4*ln(x^4+x^2+1)","A"
141,1,41,38,0.006000," ","int((2*x^3+11*x)/(x^4+2*x^2+3)^2,x)","\frac{9 \sqrt{2}\, \arctan \left(\frac{\left(2 x^{2}+2\right) \sqrt{2}}{4}\right)}{16}+\frac{18 x^{2}+10}{16 x^{4}+32 x^{2}+48}"," ",0,"1/16*(18*x^2+10)/(x^4+2*x^2+3)+9/16*2^(1/2)*arctan(1/4*(2*x^2+2)*2^(1/2))","A"
142,1,91,84,0.029000," ","int(x^5*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x)","\frac{3 \left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}} x^{4}}{10}-\frac{17 \left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}} x^{2}}{16}+\frac{21229 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{512}+\frac{1837 \left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{480}-\frac{1633 \left(2 x^{2}+5\right) \sqrt{x^{4}+5 x^{2}+3}}{256}"," ",0,"3/10*x^4*(x^4+5*x^2+3)^(3/2)-17/16*x^2*(x^4+5*x^2+3)^(3/2)+1837/480*(x^4+5*x^2+3)^(3/2)-1633/256*(2*x^2+5)*(x^4+5*x^2+3)^(1/2)+21229/512*ln(5/2+x^2+(x^4+5*x^2+3)^(1/2))","A"
143,1,74,67,0.015000," ","int(x^3*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x)","\frac{3 \left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}} x^{2}}{8}-\frac{3367 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{256}-\frac{59 \left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{48}+\frac{259 \left(2 x^{2}+5\right) \sqrt{x^{4}+5 x^{2}+3}}{128}"," ",0,"3/8*(x^4+5*x^2+3)^(3/2)*x^2-59/48*(x^4+5*x^2+3)^(3/2)+259/128*(2*x^2+5)*(x^4+5*x^2+3)^(1/2)-3367/256*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))","A"
144,1,57,60,0.011000," ","int(x*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x)","\frac{143 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{32}+\frac{\left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{2}-\frac{11 \left(2 x^{2}+5\right) \sqrt{x^{4}+5 x^{2}+3}}{16}"," ",0,"1/2*(x^4+5*x^2+3)^(3/2)-11/16*(2*x^2+5)*(x^4+5*x^2+3)^(1/2)+143/32*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))","A"
145,1,85,76,0.015000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x,x)","-\sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)+\frac{\ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{16}+\frac{3 \left(2 x^{2}+5\right) \sqrt{x^{4}+5 x^{2}+3}}{8}+\sqrt{x^{4}+5 x^{2}+3}"," ",0,"3/8*(2*x^2+5)*(x^4+5*x^2+3)^(1/2)+1/16*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))+(x^4+5*x^2+3)^(1/2)-arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)","A"
146,1,104,79,0.016000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^3,x)","-\frac{7 \sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)}{3}+\frac{19 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{4}-\frac{\left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{3 x^{2}}+\frac{7 \sqrt{x^{4}+5 x^{2}+3}}{3}+\frac{\left(2 x^{2}+5\right) \sqrt{x^{4}+5 x^{2}+3}}{6}"," ",0,"7/3*(x^4+5*x^2+3)^(1/2)+19/4*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))-7/3*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)-1/3/x^2*(x^4+5*x^2+3)^(3/2)+1/6*(2*x^2+5)*(x^4+5*x^2+3)^(1/2)","A"
147,1,121,79,0.016000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^5,x)","-\frac{77 \sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)}{72}+\frac{3 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{2}-\frac{13 \left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{36 x^{2}}-\frac{\left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{6 x^{4}}+\frac{77 \sqrt{x^{4}+5 x^{2}+3}}{72}+\frac{13 \left(2 x^{2}+5\right) \sqrt{x^{4}+5 x^{2}+3}}{72}"," ",0,"-1/6/x^4*(x^4+5*x^2+3)^(3/2)-13/36*(x^4+5*x^2+3)^(3/2)/x^2+77/72*(x^4+5*x^2+3)^(1/2)-77/72*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)+13/72*(2*x^2+5)*(x^4+5*x^2+3)^(1/2)+3/2*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))","A"
148,1,118,72,0.015000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^7,x)","\frac{13 \sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)}{108}+\frac{5 \left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{54 x^{2}}-\frac{\left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{9 x^{4}}-\frac{\left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{9 x^{6}}-\frac{13 \sqrt{x^{4}+5 x^{2}+3}}{108}-\frac{5 \left(2 x^{2}+5\right) \sqrt{x^{4}+5 x^{2}+3}}{108}"," ",0,"-1/9*(x^4+5*x^2+3)^(3/2)/x^6-1/9*(x^4+5*x^2+3)^(3/2)/x^4+5/54*(x^4+5*x^2+3)^(3/2)/x^2-13/108*(x^4+5*x^2+3)^(1/2)+13/108*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)-5/108*(2*x^2+5)*(x^4+5*x^2+3)^(1/2)","A"
149,1,135,89,0.017000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^9,x)","-\frac{871 \sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)}{10368}-\frac{335 \left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{5184 x^{2}}+\frac{67 \left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{864 x^{4}}-\frac{11 \left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{216 x^{6}}-\frac{\left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{12 x^{8}}+\frac{871 \sqrt{x^{4}+5 x^{2}+3}}{10368}+\frac{335 \left(2 x^{2}+5\right) \sqrt{x^{4}+5 x^{2}+3}}{10368}"," ",0,"-11/216*(x^4+5*x^2+3)^(3/2)/x^6+67/864*(x^4+5*x^2+3)^(3/2)/x^4-335/5184*(x^4+5*x^2+3)^(3/2)/x^2+871/10368*(x^4+5*x^2+3)^(1/2)-871/10368*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)+335/10368*(2*x^2+5)*(x^4+5*x^2+3)^(1/2)-1/12*(x^4+5*x^2+3)^(3/2)/x^8","A"
150,1,152,106,0.019000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^11,x)","\frac{2093 \sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)}{31104}+\frac{805 \left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{15552 x^{2}}-\frac{161 \left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{2592 x^{4}}+\frac{173 \left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{3240 x^{6}}-\frac{\left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{36 x^{8}}-\frac{\left(x^{4}+5 x^{2}+3\right)^{\frac{3}{2}}}{15 x^{10}}-\frac{2093 \sqrt{x^{4}+5 x^{2}+3}}{31104}-\frac{805 \left(2 x^{2}+5\right) \sqrt{x^{4}+5 x^{2}+3}}{31104}"," ",0,"-1/15*(x^4+5*x^2+3)^(3/2)/x^10-1/36*(x^4+5*x^2+3)^(3/2)/x^8+173/3240*(x^4+5*x^2+3)^(3/2)/x^6-161/2592*(x^4+5*x^2+3)^(3/2)/x^4+805/15552*(x^4+5*x^2+3)^(3/2)/x^2-2093/31104*(x^4+5*x^2+3)^(1/2)+2093/31104*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)-805/31104*(2*x^2+5)*(x^4+5*x^2+3)^(1/2)","A"
151,1,260,348,0.119000," ","int(x^4*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x)","\frac{\sqrt{x^{4}+5 x^{2}+3}\, x^{7}}{3}+\frac{11 \sqrt{x^{4}+5 x^{2}+3}\, x^{5}}{21}-\frac{26 \sqrt{x^{4}+5 x^{2}+3}\, x^{3}}{35}+\frac{13 \sqrt{x^{4}+5 x^{2}+3}\, x}{3}-\frac{78 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}+\frac{46176 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{35 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"1/3*x^7*(x^4+5*x^2+3)^(1/2)+11/21*x^5*(x^4+5*x^2+3)^(1/2)-26/35*x^3*(x^4+5*x^2+3)^(1/2)+13/3*x*(x^4+5*x^2+3)^(1/2)-78/(-30+6*13^(1/2))^(1/2)*(1-(-5/6+1/6*13^(1/2))*x^2)^(1/2)*(1-(-5/6-1/6*13^(1/2))*x^2)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*x*(-30+6*13^(1/2))^(1/2),5/6*3^(1/2)+1/6*39^(1/2))+46176/35/(-30+6*13^(1/2))^(1/2)*(1-(-5/6+1/6*13^(1/2))*x^2)^(1/2)*(1-(-5/6-1/6*13^(1/2))*x^2)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*x*(-30+6*13^(1/2))^(1/2),5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*x*(-30+6*13^(1/2))^(1/2),5/6*3^(1/2)+1/6*39^(1/2)))","A"
152,1,243,332,0.014000," ","int(x^2*(3*x^2+2)*(x^4+5*x^2+3)^(1/2),x)","\frac{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{5}}{7}+\frac{29 \sqrt{x^{4}+5 x^{2}+3}\, x^{3}}{35}-\frac{4 \sqrt{x^{4}+5 x^{2}+3}\, x}{3}+\frac{24 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{14964 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{35 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"3/7*(x^4+5*x^2+3)^(1/2)*x^5+29/35*(x^4+5*x^2+3)^(1/2)*x^3-4/3*(x^4+5*x^2+3)^(1/2)*x+24/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-14964/35/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))","A"
153,1,226,313,0.012000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(1/2),x)","\frac{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{3}}{5}+\frac{5 \sqrt{x^{4}+5 x^{2}+3}\, x}{3}+\frac{6 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}+\frac{552 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{5 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"3/5*(x^4+5*x^2+3)^(1/2)*x^3+5/3*(x^4+5*x^2+3)^(1/2)*x+6/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))+552/5/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))","A"
154,1,225,317,0.020000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^2,x)","\sqrt{x^{4}+5 x^{2}+3}\, x +\frac{96 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{2 \sqrt{x^{4}+5 x^{2}+3}}{x}-\frac{324 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"(x^4+5*x^2+3)^(1/2)*x+96/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-324/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))-2*(x^4+5*x^2+3)^(1/2)/x","A"
155,1,228,333,0.020000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(1/2)/x^4,x)","\frac{98 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{37 \sqrt{x^{4}+5 x^{2}+3}}{9 x}-\frac{2 \sqrt{x^{4}+5 x^{2}+3}}{3 x^{3}}-\frac{256 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"-37/9*(x^4+5*x^2+3)^(1/2)/x+98/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-256/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))-2/3*(x^4+5*x^2+3)^(1/2)/x^3","A"
156,1,138,105,0.033000," ","int(x^5*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x)","\frac{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{12}}{14}+\frac{253 \sqrt{x^{4}+5 x^{2}+3}\, x^{10}}{168}+\frac{539 \sqrt{x^{4}+5 x^{2}+3}\, x^{8}}{240}+\frac{645 \sqrt{x^{4}+5 x^{2}+3}\, x^{6}}{896}+\frac{5059 \sqrt{x^{4}+5 x^{2}+3}\, x^{4}}{3840}-\frac{149957 \sqrt{x^{4}+5 x^{2}+3}\, x^{2}}{21504}-\frac{368927 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{4096}+\frac{3182317 \sqrt{x^{4}+5 x^{2}+3}}{71680}"," ",0,"645/896*x^6*(x^4+5*x^2+3)^(1/2)-149957/21504*x^2*(x^4+5*x^2+3)^(1/2)-368927/4096*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))+3/14*x^12*(x^4+5*x^2+3)^(1/2)+253/168*x^10*(x^4+5*x^2+3)^(1/2)+539/240*x^8*(x^4+5*x^2+3)^(1/2)+3182317/71680*(x^4+5*x^2+3)^(1/2)+5059/3840*x^4*(x^4+5*x^2+3)^(1/2)","A"
157,1,121,88,0.016000," ","int(x^3*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x)","\frac{\sqrt{x^{4}+5 x^{2}+3}\, x^{10}}{4}+\frac{73 \sqrt{x^{4}+5 x^{2}+3}\, x^{8}}{40}+\frac{187 \sqrt{x^{4}+5 x^{2}+3}\, x^{6}}{64}+\frac{633 \sqrt{x^{4}+5 x^{2}+3}\, x^{4}}{640}+\frac{1239 \sqrt{x^{4}+5 x^{2}+3}\, x^{2}}{512}+\frac{62361 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{2048}-\frac{77229 \sqrt{x^{4}+5 x^{2}+3}}{5120}"," ",0,"187/64*(x^4+5*x^2+3)^(1/2)*x^6+1239/512*(x^4+5*x^2+3)^(1/2)*x^2+62361/2048*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))+1/4*(x^4+5*x^2+3)^(1/2)*x^10+73/40*(x^4+5*x^2+3)^(1/2)*x^8-77229/5120*(x^4+5*x^2+3)^(1/2)+633/640*(x^4+5*x^2+3)^(1/2)*x^4","A"
158,1,104,81,0.016000," ","int(x*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x)","\frac{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{8}}{10}+\frac{37 \sqrt{x^{4}+5 x^{2}+3}\, x^{6}}{16}+\frac{663 \sqrt{x^{4}+5 x^{2}+3}\, x^{4}}{160}+\frac{217 \sqrt{x^{4}+5 x^{2}+3}\, x^{2}}{128}-\frac{5577 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{512}+\frac{7581 \sqrt{x^{4}+5 x^{2}+3}}{1280}"," ",0,"3/10*(x^4+5*x^2+3)^(1/2)*x^8+37/16*(x^4+5*x^2+3)^(1/2)*x^6+663/160*(x^4+5*x^2+3)^(1/2)*x^4+217/128*(x^4+5*x^2+3)^(1/2)*x^2+7581/1280*(x^4+5*x^2+3)^(1/2)-5577/512*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))","A"
159,1,117,97,0.015000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x,x)","\frac{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{6}}{8}+\frac{151 \sqrt{x^{4}+5 x^{2}+3}\, x^{4}}{48}+\frac{1325 \sqrt{x^{4}+5 x^{2}+3}\, x^{2}}{192}-3 \sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)+\frac{2401 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{256}+\frac{687 \sqrt{x^{4}+5 x^{2}+3}}{128}"," ",0,"3/8*(x^4+5*x^2+3)^(1/2)*x^6+151/48*(x^4+5*x^2+3)^(1/2)*x^4+1325/192*(x^4+5*x^2+3)^(1/2)*x^2+687/128*(x^4+5*x^2+3)^(1/2)+2401/256*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))-3*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)","A"
160,1,117,100,0.021000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^3,x)","\frac{\sqrt{x^{4}+5 x^{2}+3}\, x^{4}}{2}+\frac{39 \sqrt{x^{4}+5 x^{2}+3}\, x^{2}}{8}-12 \sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)+\frac{609 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{32}-\frac{3 \sqrt{x^{4}+5 x^{2}+3}}{x^{2}}+\frac{271 \sqrt{x^{4}+5 x^{2}+3}}{16}"," ",0,"1/2*(x^4+5*x^2+3)^(1/2)*x^4+39/8*(x^4+5*x^2+3)^(1/2)*x^2+271/16*(x^4+5*x^2+3)^(1/2)+609/32*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))-12*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)-3*(x^4+5*x^2+3)^(1/2)/x^2","A"
161,1,117,103,0.020000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^5,x)","\frac{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{2}}{4}-\frac{127 \sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)}{8}+\frac{453 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{16}-\frac{43 \sqrt{x^{4}+5 x^{2}+3}}{4 x^{2}}-\frac{3 \sqrt{x^{4}+5 x^{2}+3}}{2 x^{4}}+\frac{83 \sqrt{x^{4}+5 x^{2}+3}}{8}"," ",0,"83/8*(x^4+5*x^2+3)^(1/2)+453/16*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))-127/8*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)-43/4*(x^4+5*x^2+3)^(1/2)/x^2-3/2*(x^4+5*x^2+3)^(1/2)/x^4+3/4*(x^4+5*x^2+3)^(1/2)*x^2","A"
162,1,117,103,0.022000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^7,x)","-\frac{527 \sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)}{72}+\frac{49 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{4}-\frac{47 \sqrt{x^{4}+5 x^{2}+3}}{4 x^{2}}-\frac{31 \sqrt{x^{4}+5 x^{2}+3}}{6 x^{4}}-\frac{\sqrt{x^{4}+5 x^{2}+3}}{x^{6}}+\frac{3 \sqrt{x^{4}+5 x^{2}+3}}{2}"," ",0,"49/4*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))-527/72*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)-47/4*(x^4+5*x^2+3)^(1/2)/x^2-(x^4+5*x^2+3)^(1/2)/x^6-31/6*(x^4+5*x^2+3)^(1/2)/x^4+3/2*(x^4+5*x^2+3)^(1/2)","A"
163,1,294,373,0.021000," ","int(x^4*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x)","\frac{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{11}}{13}+\frac{236 \sqrt{x^{4}+5 x^{2}+3}\, x^{9}}{143}+\frac{1090 \sqrt{x^{4}+5 x^{2}+3}\, x^{7}}{429}+\frac{356 \sqrt{x^{4}+5 x^{2}+3}\, x^{5}}{429}+\frac{1251 \sqrt{x^{4}+5 x^{2}+3}\, x^{3}}{715}-\frac{4210 \sqrt{x^{4}+5 x^{2}+3}\, x}{429}+\frac{25260 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{143 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{2120676 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{715 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"3/13*x^11*(x^4+5*x^2+3)^(1/2)+236/143*x^9*(x^4+5*x^2+3)^(1/2)+1090/429*(x^4+5*x^2+3)^(1/2)*x^7+356/429*(x^4+5*x^2+3)^(1/2)*x^5+1251/715*(x^4+5*x^2+3)^(1/2)*x^3-4210/429*(x^4+5*x^2+3)^(1/2)*x+25260/143/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-2120676/715/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))","A"
164,1,277,355,0.017000," ","int(x^2*(3*x^2+2)*(x^4+5*x^2+3)^(3/2),x)","\frac{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{9}}{11}+\frac{202 \sqrt{x^{4}+5 x^{2}+3}\, x^{7}}{99}+\frac{2378 \sqrt{x^{4}+5 x^{2}+3}\, x^{5}}{693}+\frac{478 \sqrt{x^{4}+5 x^{2}+3}\, x^{3}}{385}+\frac{353 \sqrt{x^{4}+5 x^{2}+3}\, x}{99}-\frac{706 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{11 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}+\frac{399592 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{385 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"3/11*(x^4+5*x^2+3)^(1/2)*x^9+202/99*(x^4+5*x^2+3)^(1/2)*x^7+2378/693*(x^4+5*x^2+3)^(1/2)*x^5+478/385*(x^4+5*x^2+3)^(1/2)*x^3+353/99*(x^4+5*x^2+3)^(1/2)*x-706/11/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))+399592/385/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))","A"
165,1,260,335,0.014000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(3/2),x)","\frac{\sqrt{x^{4}+5 x^{2}+3}\, x^{7}}{3}+\frac{8 \sqrt{x^{4}+5 x^{2}+3}\, x^{5}}{3}+\frac{26 \sqrt{x^{4}+5 x^{2}+3}\, x^{3}}{5}+\frac{8 \sqrt{x^{4}+5 x^{2}+3}\, x}{3}+\frac{60 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{2436 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{5 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"1/3*(x^4+5*x^2+3)^(1/2)*x^7+8/3*(x^4+5*x^2+3)^(1/2)*x^5+26/5*(x^4+5*x^2+3)^(1/2)*x^3+8/3*(x^4+5*x^2+3)^(1/2)*x+60/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-2436/5/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))","A"
166,1,260,339,0.019000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^2,x)","\frac{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{5}}{7}+\frac{134 \sqrt{x^{4}+5 x^{2}+3}\, x^{3}}{35}+10 \sqrt{x^{4}+5 x^{2}+3}\, x +\frac{342 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{6 \sqrt{x^{4}+5 x^{2}+3}}{x}-\frac{29664 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{35 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"3/7*(x^4+5*x^2+3)^(1/2)*x^5+134/35*(x^4+5*x^2+3)^(1/2)*x^3+10*(x^4+5*x^2+3)^(1/2)*x+342/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-29664/35/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))-6*(x^4+5*x^2+3)^(1/2)/x","A"
167,1,260,341,0.020000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^4,x)","\frac{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{3}}{5}+\frac{20 \sqrt{x^{4}+5 x^{2}+3}\, x}{3}+\frac{780 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{67 \sqrt{x^{4}+5 x^{2}+3}}{3 x}-\frac{2 \sqrt{x^{4}+5 x^{2}+3}}{x^{3}}-\frac{11388 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{5 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"-67/3*(x^4+5*x^2+3)^(1/2)/x+3/5*(x^4+5*x^2+3)^(1/2)*x^3+20/3*(x^4+5*x^2+3)^(1/2)*x+780/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-11388/5/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))-2*(x^4+5*x^2+3)^(1/2)/x^3","A"
168,1,259,357,0.021000," ","int((3*x^2+2)*(x^4+5*x^2+3)^(3/2)/x^6,x)","\sqrt{x^{4}+5 x^{2}+3}\, x +\frac{618 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{392 \sqrt{x^{4}+5 x^{2}+3}}{15 x}-\frac{7 \sqrt{x^{4}+5 x^{2}+3}}{x^{3}}-\frac{6 \sqrt{x^{4}+5 x^{2}+3}}{5 x^{5}}-\frac{8664 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{5 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"-7*(x^4+5*x^2+3)^(1/2)/x^3-392/15*(x^4+5*x^2+3)^(1/2)/x+(x^4+5*x^2+3)^(1/2)*x+618/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-8664/5/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))-6/5/x^5*(x^4+5*x^2+3)^(1/2)","A"
169,1,286,135,0.030000," ","int(x^5*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, B \,x^{4}}{6 c}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, A \,x^{2}}{4 c}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, B b \,x^{2}}{24 c^{2}}-\frac{A a \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 c^{\frac{3}{2}}}+\frac{3 A \,b^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 c^{\frac{5}{2}}}+\frac{3 B a b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{8 c^{\frac{5}{2}}}-\frac{5 B \,b^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{7}{2}}}-\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, A b}{8 c^{2}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, B a}{3 c^{2}}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, B \,b^{2}}{16 c^{3}}"," ",0,"1/6*B*x^4*(c*x^4+b*x^2+a)^(1/2)/c-5/24*B*b/c^2*x^2*(c*x^4+b*x^2+a)^(1/2)+5/16*B*b^2/c^3*(c*x^4+b*x^2+a)^(1/2)-5/32*B*b^3/c^(7/2)*ln((1/2*b+c*x^2)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+3/8*B*b/c^(5/2)*a*ln((1/2*b+c*x^2)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/3*B*a/c^2*(c*x^4+b*x^2+a)^(1/2)+1/4*A*x^2/c*(c*x^4+b*x^2+a)^(1/2)-3/8*A*b/c^2*(c*x^4+b*x^2+a)^(1/2)+3/16*A*b^2/c^(5/2)*ln((1/2*b+c*x^2)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/4*A*a/c^(3/2)*ln((1/2*b+c*x^2)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))","B"
170,1,176,86,0.015000," ","int(x^3*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, B \,x^{2}}{4 c}-\frac{A b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 c^{\frac{3}{2}}}-\frac{B a \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 c^{\frac{3}{2}}}+\frac{3 B \,b^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 c^{\frac{5}{2}}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, A}{2 c}-\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, B b}{8 c^{2}}"," ",0,"1/4*B*x^2/c*(c*x^4+b*x^2+a)^(1/2)-3/8*B*b/c^2*(c*x^4+b*x^2+a)^(1/2)+3/16*B*b^2/c^(5/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/4*B*a/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+1/2*A/c*(c*x^4+b*x^2+a)^(1/2)-1/4*A*b/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))","B"
171,1,93,62,0.012000," ","int(x*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x)","\frac{A \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2 \sqrt{c}}-\frac{B b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 c^{\frac{3}{2}}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, B}{2 c}"," ",0,"1/2*B*(c*x^4+b*x^2+a)^(1/2)/c-1/4*B*b/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+1/2*A*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)","A"
172,1,76,70,0.013000," ","int((B*x^2+A)/x/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{A \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}}+\frac{B \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2 \sqrt{c}}"," ",0,"1/2*B*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)-1/2*A/a^(1/2)*ln((2*a+b*x^2+2*a^(1/2)*(c*x^4+b*x^2+a)^(1/2))/x^2)","A"
173,1,104,66,0.018000," ","int((B*x^2+A)/x^3/(c*x^4+b*x^2+a)^(1/2),x)","\frac{A b \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}}}-\frac{B \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}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, A}{2 a \,x^{2}}"," ",0,"-1/2*B/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-1/2*A*(c*x^4+b*x^2+a)^(1/2)/a/x^2+1/4*A*b/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
174,1,194,106,0.019000," ","int((B*x^2+A)/x^5/(c*x^4+b*x^2+a)^(1/2),x)","\frac{A c \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}}}-\frac{3 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)}{16 a^{\frac{5}{2}}}+\frac{B b \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}}}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, A b}{8 a^{2} x^{2}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, B}{2 a \,x^{2}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, A}{4 a \,x^{4}}"," ",0,"-1/4*A*(c*x^4+b*x^2+a)^(1/2)/a/x^4+3/8*A*b/a^2/x^2*(c*x^4+b*x^2+a)^(1/2)-3/16*A*b^2/a^(5/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+1/4*A*c/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-1/2*B/a/x^2*(c*x^4+b*x^2+a)^(1/2)+1/4*B*b/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
175,1,311,155,0.020000," ","int((B*x^2+A)/x^7/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{3 A b c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{8 a^{\frac{5}{2}}}+\frac{5 A \,b^{3} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{32 a^{\frac{7}{2}}}+\frac{B c \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}}}-\frac{3 B \,b^{2} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{16 a^{\frac{5}{2}}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, A c}{3 a^{2} x^{2}}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, A \,b^{2}}{16 a^{3} x^{2}}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, B b}{8 a^{2} x^{2}}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, A b}{24 a^{2} x^{4}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, B}{4 a \,x^{4}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, A}{6 a \,x^{6}}"," ",0,"-1/6*A*(c*x^4+b*x^2+a)^(1/2)/a/x^6+5/24*A*b/a^2/x^4*(c*x^4+b*x^2+a)^(1/2)-5/16*A*b^2/a^3/x^2*(c*x^4+b*x^2+a)^(1/2)+5/32*A*b^3/a^(7/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-3/8*A*b/a^(5/2)*c*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+1/3*A/a^2*c/x^2*(c*x^4+b*x^2+a)^(1/2)-1/4*B/a/x^4*(c*x^4+b*x^2+a)^(1/2)+3/8*B*b/a^2/x^2*(c*x^4+b*x^2+a)^(1/2)-3/16*B*b^2/a^(5/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+1/4*B*c/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
176,1,815,391,0.023000," ","int(x^4*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x)","\left(\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a b}{3 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right) c}-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x}{3 c}\right) A +\left(\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{3}}{5 c}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a b \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{15 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}-\frac{\left(-\frac{3 a}{5 c}+\frac{8 b^{2}}{15 c^{2}}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}-\frac{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b x}{15 c^{2}}\right) B"," ",0,"B*(1/5/c*x^3*(c*x^4+b*x^2+a)^(1/2)-4/15*b/c^2*x*(c*x^4+b*x^2+a)^(1/2)+1/15*b/c^2*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*x*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-1/2*(-3/5/c*a+8/15*b^2/c^2)*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*x*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-EllipticE(1/2*x*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))))+A*(1/3/c*x*(c*x^4+b*x^2+a)^(1/2)-1/12/c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*x*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))+1/3*b/c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*x*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-EllipticE(1/2*x*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))))","B"
177,1,607,328,0.011000," ","int(x^2*(B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) A a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\left(\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a b}{3 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right) c}-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x}{3 c}\right) B"," ",0,"B*(1/3*(c*x^4+b*x^2+a)^(1/2)/c*x-1/12/c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+1/3*b/c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))))-1/2*A*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
178,1,362,283,0.010000," ","int((B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, A \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) B a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}"," ",0,"-1/2*B*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))+1/4*A*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))","A"
179,1,386,310,0.020000," ","int((B*x^2+A)/x^2/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, B \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}+\left(-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) c}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{a x}\right) A"," ",0,"1/4*B*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+A*(-1/a*(c*x^4+b*x^2+a)^(1/2)/x-1/2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))))","A"
180,1,656,364,0.023000," ","int((B*x^2+A)/x^4/(c*x^4+b*x^2+a)^(1/2),x)","\left(\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) b c}{3 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right) a}-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, a}+\frac{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{3 a^{2} x}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{3 a \,x^{3}}\right) A +\left(-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) c}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{a x}\right) B"," ",0,"B*(-(c*x^4+b*x^2+a)^(1/2)/a/x-1/2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))))+A*(-1/3/a*(c*x^4+b*x^2+a)^(1/2)/x^3+2/3/a^2*b*(c*x^4+b*x^2+a)^(1/2)/x-1/12/a*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+1/3*b*c/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))))","A"
181,1,87,80,0.019000," ","int(x^7*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x)","\frac{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{6}}{8}-\frac{89 \sqrt{x^{4}+5 x^{2}+3}\, x^{4}}{48}+\frac{1901 \sqrt{x^{4}+5 x^{2}+3}\, x^{2}}{192}+\frac{32801 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{256}-\frac{8081 \sqrt{x^{4}+5 x^{2}+3}}{128}"," ",0,"3/8*(x^4+5*x^2+3)^(1/2)*x^6-89/48*(x^4+5*x^2+3)^(1/2)*x^4+1901/192*(x^4+5*x^2+3)^(1/2)*x^2-8081/128*(x^4+5*x^2+3)^(1/2)+32801/256*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))","A"
182,1,70,63,0.014000," ","int(x^5*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x)","\frac{\sqrt{x^{4}+5 x^{2}+3}\, x^{4}}{2}-\frac{21 \sqrt{x^{4}+5 x^{2}+3}\, x^{2}}{8}-\frac{1083 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{32}+\frac{267 \sqrt{x^{4}+5 x^{2}+3}}{16}"," ",0,"1/2*(x^4+5*x^2+3)^(1/2)*x^4-21/8*(x^4+5*x^2+3)^(1/2)*x^2+267/16*(x^4+5*x^2+3)^(1/2)-1083/32*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))","A"
183,1,53,46,0.013000," ","int(x^3*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x)","\frac{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{2}}{4}+\frac{149 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{16}-\frac{37 \sqrt{x^{4}+5 x^{2}+3}}{8}"," ",0,"3/4*(x^4+5*x^2+3)^(1/2)*x^2-37/8*(x^4+5*x^2+3)^(1/2)+149/16*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))","A"
184,1,36,39,0.012000," ","int(x*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x)","-\frac{11 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{4}+\frac{3 \sqrt{x^{4}+5 x^{2}+3}}{2}"," ",0,"3/2*(x^4+5*x^2+3)^(1/2)-11/4*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))","A"
185,1,52,55,0.012000," ","int((3*x^2+2)/x/(x^4+5*x^2+3)^(1/2),x)","-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)}{3}+\frac{3 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{2}"," ",0,"3/2*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))-1/3*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)","A"
186,1,49,48,0.015000," ","int((3*x^2+2)/x^3/(x^4+5*x^2+3)^(1/2),x)","-\frac{2 \sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)}{9}-\frac{\sqrt{x^{4}+5 x^{2}+3}}{3 x^{2}}"," ",0,"-2/9*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)-1/3*(x^4+5*x^2+3)^(1/2)/x^2","A"
187,1,66,65,0.013000," ","int((3*x^2+2)/x^5/(x^4+5*x^2+3)^(1/2),x)","\frac{\sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)}{8}-\frac{\sqrt{x^{4}+5 x^{2}+3}}{12 x^{2}}-\frac{\sqrt{x^{4}+5 x^{2}+3}}{6 x^{4}}"," ",0,"1/8*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)-1/6*(x^4+5*x^2+3)^(1/2)/x^4-1/12*(x^4+5*x^2+3)^(1/2)/x^2","A"
188,1,83,82,0.017000," ","int((3*x^2+2)/x^7/(x^4+5*x^2+3)^(1/2),x)","-\frac{61 \sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)}{648}+\frac{13 \sqrt{x^{4}+5 x^{2}+3}}{108 x^{2}}-\frac{\sqrt{x^{4}+5 x^{2}+3}}{54 x^{4}}-\frac{\sqrt{x^{4}+5 x^{2}+3}}{9 x^{6}}"," ",0,"-61/648*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)-1/9*(x^4+5*x^2+3)^(1/2)/x^6-1/54*(x^4+5*x^2+3)^(1/2)/x^4+13/108*(x^4+5*x^2+3)^(1/2)/x^2","A"
189,1,226,325,0.018000," ","int(x^4*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x)","\frac{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{3}}{5}-\frac{10 \sqrt{x^{4}+5 x^{2}+3}\, x}{3}+\frac{60 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{5028 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{5 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"3/5*(x^4+5*x^2+3)^(1/2)*x^3-10/3*(x^4+5*x^2+3)^(1/2)*x+60/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-5028/5/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))","A"
190,1,208,307,0.013000," ","int(x^2*(3*x^2+2)/(x^4+5*x^2+3)^(1/2),x)","\sqrt{x^{4}+5 x^{2}+3}\, x -\frac{18 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}+\frac{288 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"(x^4+5*x^2+3)^(1/2)*x-18/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))+288/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))","A"
191,1,194,293,0.012000," ","int((3*x^2+2)/(x^4+5*x^2+3)^(1/2),x)","\frac{12 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{108 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"-108/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))+12/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))","A"
192,1,211,310,0.023000," ","int((3*x^2+2)/x^2/(x^4+5*x^2+3)^(1/2),x)","\frac{18 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{2 \sqrt{x^{4}+5 x^{2}+3}}{3 x}-\frac{24 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{\sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"18/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-2/3*(x^4+5*x^2+3)^(1/2)/x-24/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))","A"
193,1,228,327,0.018000," ","int((3*x^2+2)/x^4/(x^4+5*x^2+3)^(1/2),x)","-\frac{4 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{3 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{7 \sqrt{x^{4}+5 x^{2}+3}}{27 x}-\frac{2 \sqrt{x^{4}+5 x^{2}+3}}{9 x^{3}}-\frac{28 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{3 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}"," ",0,"-7/27*(x^4+5*x^2+3)^(1/2)/x-28/3/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))-2/9*(x^4+5*x^2+3)^(1/2)/x^3-4/3/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))","A"
194,1,91,63,0.022000," ","int(x^5*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x)","\frac{3 x^{4}}{2 \sqrt{x^{4}+5 x^{2}+3}}+\frac{41 x^{2}}{4 \sqrt{x^{4}+5 x^{2}+3}}-\frac{41 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{4}-\frac{133}{8 \sqrt{x^{4}+5 x^{2}+3}}+\frac{\frac{665 x^{2}}{52}+\frac{3325}{104}}{\sqrt{x^{4}+5 x^{2}+3}}"," ",0,"3/2*x^4/(x^4+5*x^2+3)^(1/2)+41/4*x^2/(x^4+5*x^2+3)^(1/2)-133/8/(x^4+5*x^2+3)^(1/2)+665/104*(2*x^2+5)/(x^4+5*x^2+3)^(1/2)-41/4*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))","A"
195,1,95,46,0.013000," ","int(x^3*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x)","-\frac{3 x^{2}}{2 \sqrt{x^{4}+5 x^{2}+3}}+\frac{3 \ln \left(x^{2}+\frac{5}{2}+\sqrt{x^{4}+5 x^{2}+3}\right)}{2}+\frac{15}{4 \sqrt{x^{4}+5 x^{2}+3}}-\frac{75 \left(2 x^{2}+5\right)}{52 \sqrt{x^{4}+5 x^{2}+3}}+\frac{\frac{10 x^{2}}{13}+\frac{12}{13}}{\sqrt{x^{4}+5 x^{2}+3}}"," ",0,"-3/2/(x^4+5*x^2+3)^(1/2)*x^2+15/4/(x^4+5*x^2+3)^(1/2)-75/52*(2*x^2+5)/(x^4+5*x^2+3)^(1/2)+3/2*ln(x^2+5/2+(x^4+5*x^2+3)^(1/2))+2/13/(x^4+5*x^2+3)^(1/2)*(5*x^2+6)","B"
196,1,22,21,0.006000," ","int(x*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x)","\frac{11 x^{2}+8}{13 \sqrt{x^{4}+5 x^{2}+3}}"," ",0,"1/13*(11*x^2+8)/(x^4+5*x^2+3)^(1/2)","A"
197,1,67,52,0.019000," ","int((3*x^2+2)/x/(x^4+5*x^2+3)^(3/2),x)","-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)}{9}-\frac{4 \left(2 x^{2}+5\right)}{39 \sqrt{x^{4}+5 x^{2}+3}}+\frac{1}{3 \sqrt{x^{4}+5 x^{2}+3}}"," ",0,"-4/39*(2*x^2+5)/(x^4+5*x^2+3)^(1/2)+1/3/(x^4+5*x^2+3)^(1/2)-1/9*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)","A"
198,1,84,72,0.016000," ","int((3*x^2+2)/x^3/(x^4+5*x^2+3)^(3/2),x)","\frac{\sqrt{3}\, \arctanh \left(\frac{\left(5 x^{2}+6\right) \sqrt{3}}{6 \sqrt{x^{4}+5 x^{2}+3}}\right)}{9}-\frac{1}{3 \sqrt{x^{4}+5 x^{2}+3}\, x^{2}}-\frac{1}{3 \sqrt{x^{4}+5 x^{2}+3}}-\frac{2 x^{2}+5}{39 \sqrt{x^{4}+5 x^{2}+3}}"," ",0,"-1/3/(x^4+5*x^2+3)^(1/2)-1/39*(2*x^2+5)/(x^4+5*x^2+3)^(1/2)+1/9*arctanh(1/6*(5*x^2+6)*3^(1/2)/(x^4+5*x^2+3)^(1/2))*3^(1/2)-1/3/x^2/(x^4+5*x^2+3)^(1/2)","A"
199,1,240,332,0.024000," ","int(x^4*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x)","\frac{198 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{13 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{6 \left(\frac{19}{26} x^{3}+\frac{15}{26} x \right)}{\sqrt{x^{4}+5 x^{2}+3}}-\frac{3096 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{13 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}-\frac{4 \left(-\frac{5}{26} x^{3}-\frac{3}{13} x \right)}{\sqrt{x^{4}+5 x^{2}+3}}"," ",0,"-6*(19/26*x^3+15/26*x)/(x^4+5*x^2+3)^(1/2)+198/13/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-3096/13/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))-4*(-5/26*x^3-3/13*x)/(x^4+5*x^2+3)^(1/2)","A"
200,1,240,315,0.016000," ","int(x^2*(3*x^2+2)/(x^4+5*x^2+3)^(3/2),x)","-\frac{48 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{13 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{6 \left(-\frac{5}{26} x^{3}-\frac{3}{13} x \right)}{\sqrt{x^{4}+5 x^{2}+3}}+\frac{396 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{13 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}-\frac{4 \left(\frac{1}{13} x^{3}+\frac{5}{26} x \right)}{\sqrt{x^{4}+5 x^{2}+3}}"," ",0,"-6*(-5/26*x^3-3/13*x)/(x^4+5*x^2+3)^(1/2)-48/13/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))+396/13/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))-4*(1/13*x^3+5/26*x)/(x^4+5*x^2+3)^(1/2)","A"
201,1,240,314,0.017000," ","int((3*x^2+2)/(x^4+5*x^2+3)^(3/2),x)","\frac{66 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{13 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{6 \left(\frac{1}{13} x^{3}+\frac{5}{26} x \right)}{\sqrt{x^{4}+5 x^{2}+3}}-\frac{96 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{13 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}-\frac{4 \left(-\frac{5}{78} x^{3}-\frac{19}{78} x \right)}{\sqrt{x^{4}+5 x^{2}+3}}"," ",0,"-6*(1/13*x^3+5/26*x)/(x^4+5*x^2+3)^(1/2)+66/13/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-96/13/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))-4*(-19/78*x-5/78*x^3)/(x^4+5*x^2+3)^(1/2)","A"
202,1,257,334,0.026000," ","int((3*x^2+2)/x^2/(x^4+5*x^2+3)^(3/2),x)","-\frac{16 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{13 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}-\frac{2 \sqrt{x^{4}+5 x^{2}+3}}{9 x}-\frac{6 \left(-\frac{5}{78} x^{3}-\frac{19}{78} x \right)}{\sqrt{x^{4}+5 x^{2}+3}}-\frac{76 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{13 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}-\frac{4 \left(\frac{19}{234} x^{3}+\frac{40}{117} x \right)}{\sqrt{x^{4}+5 x^{2}+3}}"," ",0,"-6*(-5/78*x^3-19/78*x)/(x^4+5*x^2+3)^(1/2)-16/13/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-76/13/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))-2/9*(x^4+5*x^2+3)^(1/2)/x-4*(19/234*x^3+40/117*x)/(x^4+5*x^2+3)^(1/2)","A"
203,1,274,350,0.023000," ","int((3*x^2+2)/x^4/(x^4+5*x^2+3)^(3/2),x)","-\frac{10 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)}{117 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}}+\frac{23 \sqrt{x^{4}+5 x^{2}+3}}{81 x}-\frac{2 \sqrt{x^{4}+5 x^{2}+3}}{27 x^{3}}-\frac{6 \left(\frac{19}{234} x^{3}+\frac{40}{117} x \right)}{\sqrt{x^{4}+5 x^{2}+3}}+\frac{1064 \sqrt{-\left(-\frac{5}{6}+\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{6}-\frac{\sqrt{13}}{6}\right) x^{2}+1}\, \left(-\EllipticE \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)+\EllipticF \left(\frac{\sqrt{-30+6 \sqrt{13}}\, x}{6}, \frac{5 \sqrt{3}}{6}+\frac{\sqrt{39}}{6}\right)\right)}{117 \sqrt{-30+6 \sqrt{13}}\, \sqrt{x^{4}+5 x^{2}+3}\, \left(\sqrt{13}+5\right)}-\frac{4 \left(-\frac{40}{351} x^{3}-\frac{343}{702} x \right)}{\sqrt{x^{4}+5 x^{2}+3}}"," ",0,"23/81*(x^4+5*x^2+3)^(1/2)/x-6*(19/234*x^3+40/117*x)/(x^4+5*x^2+3)^(1/2)-10/117/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)*EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))+1064/117/(-30+6*13^(1/2))^(1/2)*(-(-5/6+1/6*13^(1/2))*x^2+1)^(1/2)*(-(-5/6-1/6*13^(1/2))*x^2+1)^(1/2)/(x^4+5*x^2+3)^(1/2)/(13^(1/2)+5)*(EllipticF(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2))-EllipticE(1/6*(-30+6*13^(1/2))^(1/2)*x,5/6*3^(1/2)+1/6*39^(1/2)))-2/27*(x^4+5*x^2+3)^(1/2)/x^3-4*(-40/351*x^3-343/702*x)/(x^4+5*x^2+3)^(1/2)","A"
204,0,0,245,0.128000," ","int((f*x)^(3/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(1/2),x)","\int \left(f x \right)^{\frac{3}{2}} \left(e \,x^{2}+d \right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int((f*x)^(3/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(1/2),x)","F"
205,0,0,245,0.067000," ","int((f*x)^(1/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(1/2),x)","\int \sqrt{f x}\, \left(e \,x^{2}+d \right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int((f*x)^(1/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(1/2),x)","F"
206,0,0,245,0.059000," ","int((e*x^2+d)*(c*x^4+b*x^2+a)^(1/2)/(f*x)^(1/2),x)","\int \frac{\left(e \,x^{2}+d \right) \sqrt{c \,x^{4}+b \,x^{2}+a}}{\sqrt{f x}}\, dx"," ",0,"int((e*x^2+d)*(c*x^4+b*x^2+a)^(1/2)/(f*x)^(1/2),x)","F"
207,0,0,245,0.062000," ","int((e*x^2+d)*(c*x^4+b*x^2+a)^(1/2)/(f*x)^(3/2),x)","\int \frac{\left(e \,x^{2}+d \right) \sqrt{c \,x^{4}+b \,x^{2}+a}}{\left(f x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x^2+d)*(c*x^4+b*x^2+a)^(1/2)/(f*x)^(3/2),x)","F"
208,0,0,247,0.062000," ","int((f*x)^(3/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(3/2),x)","\int \left(f x \right)^{\frac{3}{2}} \left(e \,x^{2}+d \right) \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}\, dx"," ",0,"int((f*x)^(3/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(3/2),x)","F"
209,0,0,247,0.069000," ","int((f*x)^(1/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(3/2),x)","\int \sqrt{f x}\, \left(e \,x^{2}+d \right) \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}\, dx"," ",0,"int((f*x)^(1/2)*(e*x^2+d)*(c*x^4+b*x^2+a)^(3/2),x)","F"
210,0,0,247,0.058000," ","int((e*x^2+d)*(c*x^4+b*x^2+a)^(3/2)/(f*x)^(1/2),x)","\int \frac{\left(e \,x^{2}+d \right) \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}{\sqrt{f x}}\, dx"," ",0,"int((e*x^2+d)*(c*x^4+b*x^2+a)^(3/2)/(f*x)^(1/2),x)","F"
211,0,0,247,0.065000," ","int((e*x^2+d)*(c*x^4+b*x^2+a)^(3/2)/(f*x)^(3/2),x)","\int \frac{\left(e \,x^{2}+d \right) \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}{\left(f x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x^2+d)*(c*x^4+b*x^2+a)^(3/2)/(f*x)^(3/2),x)","F"
212,0,0,245,0.051000," ","int((f*x)^(3/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","\int \frac{\left(f x \right)^{\frac{3}{2}} \left(e \,x^{2}+d \right)}{\sqrt{c \,x^{4}+b \,x^{2}+a}}\, dx"," ",0,"int((f*x)^(3/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","F"
213,0,0,245,0.027000," ","int((f*x)^(1/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","\int \frac{\sqrt{f x}\, \left(e \,x^{2}+d \right)}{\sqrt{c \,x^{4}+b \,x^{2}+a}}\, dx"," ",0,"int((f*x)^(1/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","F"
214,0,0,245,0.025000," ","int((e*x^2+d)/(f*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2),x)","\int \frac{e \,x^{2}+d}{\sqrt{f x}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}\, dx"," ",0,"int((e*x^2+d)/(f*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2),x)","F"
215,0,0,245,0.058000," ","int((e*x^2+d)/(f*x)^(3/2)/(c*x^4+b*x^2+a)^(1/2),x)","\int \frac{e \,x^{2}+d}{\left(f x \right)^{\frac{3}{2}} \sqrt{c \,x^{4}+b \,x^{2}+a}}\, dx"," ",0,"int((e*x^2+d)/(f*x)^(3/2)/(c*x^4+b*x^2+a)^(1/2),x)","F"
216,0,0,251,0.027000," ","int((f*x)^(3/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","\int \frac{\left(f x \right)^{\frac{3}{2}} \left(e \,x^{2}+d \right)}{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f*x)^(3/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","F"
217,0,0,251,0.026000," ","int((f*x)^(1/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","\int \frac{\sqrt{f x}\, \left(e \,x^{2}+d \right)}{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f*x)^(1/2)*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","F"
218,0,0,251,0.039000," ","int((e*x^2+d)/(f*x)^(1/2)/(c*x^4+b*x^2+a)^(3/2),x)","\int \frac{e \,x^{2}+d}{\sqrt{f x}\, \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x^2+d)/(f*x)^(1/2)/(c*x^4+b*x^2+a)^(3/2),x)","F"
219,0,0,251,0.134000," ","int((e*x^2+d)/(f*x)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x)","\int \frac{e \,x^{2}+d}{\left(f x \right)^{\frac{3}{2}} \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x^2+d)/(f*x)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x)","F"
220,1,1935,243,0.009000," ","int((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^3,x)","\frac{\left(c^{3} e \,m^{7} x^{14}+49 c^{3} e \,m^{6} x^{14}+3 b \,c^{2} e \,m^{7} x^{12}+c^{3} d \,m^{7} x^{12}+973 c^{3} e \,m^{5} x^{14}+153 b \,c^{2} e \,m^{6} x^{12}+51 c^{3} d \,m^{6} x^{12}+10045 c^{3} e \,m^{4} x^{14}+3 a \,c^{2} e \,m^{7} x^{10}+3 b^{2} c e \,m^{7} x^{10}+3 b \,c^{2} d \,m^{7} x^{10}+3135 b \,c^{2} e \,m^{5} x^{12}+1045 c^{3} d \,m^{5} x^{12}+57379 c^{3} e \,m^{3} x^{14}+159 a \,c^{2} e \,m^{6} x^{10}+159 b^{2} c e \,m^{6} x^{10}+159 b \,c^{2} d \,m^{6} x^{10}+33165 b \,c^{2} e \,m^{4} x^{12}+11055 c^{3} d \,m^{4} x^{12}+177331 c^{3} e \,m^{2} x^{14}+6 a b c e \,m^{7} x^{8}+3 a \,c^{2} d \,m^{7} x^{8}+3375 a \,c^{2} e \,m^{5} x^{10}+b^{3} e \,m^{7} x^{8}+3 b^{2} c d \,m^{7} x^{8}+3375 b^{2} c e \,m^{5} x^{10}+3375 b \,c^{2} d \,m^{5} x^{10}+193017 b \,c^{2} e \,m^{3} x^{12}+64339 c^{3} d \,m^{3} x^{12}+264207 c^{3} e m \,x^{14}+330 a b c e \,m^{6} x^{8}+165 a \,c^{2} d \,m^{6} x^{8}+36795 a \,c^{2} e \,m^{4} x^{10}+55 b^{3} e \,m^{6} x^{8}+165 b^{2} c d \,m^{6} x^{8}+36795 b^{2} c e \,m^{4} x^{10}+36795 b \,c^{2} d \,m^{4} x^{10}+604827 b \,c^{2} e \,m^{2} x^{12}+201609 c^{3} d \,m^{2} x^{12}+135135 e \,c^{3} x^{14}+3 a^{2} c e \,m^{7} x^{6}+3 a \,b^{2} e \,m^{7} x^{6}+6 a b c d \,m^{7} x^{6}+7278 a b c e \,m^{5} x^{8}+3639 a \,c^{2} d \,m^{5} x^{8}+219417 a \,c^{2} e \,m^{3} x^{10}+b^{3} d \,m^{7} x^{6}+1213 b^{3} e \,m^{5} x^{8}+3639 b^{2} c d \,m^{5} x^{8}+219417 b^{2} c e \,m^{3} x^{10}+219417 b \,c^{2} d \,m^{3} x^{10}+909765 b \,c^{2} e m \,x^{12}+303255 c^{3} d m \,x^{12}+171 a^{2} c e \,m^{6} x^{6}+171 a \,b^{2} e \,m^{6} x^{6}+342 a b c d \,m^{6} x^{6}+82338 a b c e \,m^{4} x^{8}+41169 a \,c^{2} d \,m^{4} x^{8}+700461 a \,c^{2} e \,m^{2} x^{10}+57 b^{3} d \,m^{6} x^{6}+13723 b^{3} e \,m^{4} x^{8}+41169 b^{2} c d \,m^{4} x^{8}+700461 b^{2} c e \,m^{2} x^{10}+700461 b \,c^{2} d \,m^{2} x^{10}+467775 b \,c^{2} e \,x^{12}+155925 c^{3} d \,x^{12}+3 a^{2} b e \,m^{7} x^{4}+3 a^{2} c d \,m^{7} x^{4}+3927 a^{2} c e \,m^{5} x^{6}+3 a \,b^{2} d \,m^{7} x^{4}+3927 a \,b^{2} e \,m^{5} x^{6}+7854 a b c d \,m^{5} x^{6}+507282 a b c e \,m^{3} x^{8}+253641 a \,c^{2} d \,m^{3} x^{8}+1067445 a \,c^{2} e m \,x^{10}+1309 b^{3} d \,m^{5} x^{6}+84547 b^{3} e \,m^{3} x^{8}+253641 b^{2} c d \,m^{3} x^{8}+1067445 b^{2} c e m \,x^{10}+1067445 b \,c^{2} d m \,x^{10}+177 a^{2} b e \,m^{6} x^{4}+177 a^{2} c d \,m^{6} x^{4}+46431 a^{2} c e \,m^{4} x^{6}+177 a \,b^{2} d \,m^{6} x^{4}+46431 a \,b^{2} e \,m^{4} x^{6}+92862 a b c d \,m^{4} x^{6}+1662558 a b c e \,m^{2} x^{8}+831279 a \,c^{2} d \,m^{2} x^{8}+552825 a \,c^{2} e \,x^{10}+15477 b^{3} d \,m^{4} x^{6}+277093 b^{3} e \,m^{2} x^{8}+831279 b^{2} c d \,m^{2} x^{8}+552825 b^{2} c e \,x^{10}+552825 b \,c^{2} d \,x^{10}+a^{3} e \,m^{7} x^{2}+3 a^{2} b d \,m^{7} x^{2}+4239 a^{2} b e \,m^{5} x^{4}+4239 a^{2} c d \,m^{5} x^{4}+299145 a^{2} c e \,m^{3} x^{6}+4239 a \,b^{2} d \,m^{5} x^{4}+299145 a \,b^{2} e \,m^{3} x^{6}+598290 a b c d \,m^{3} x^{6}+2582010 a b c e m \,x^{8}+1291005 a \,c^{2} d m \,x^{8}+99715 b^{3} d \,m^{3} x^{6}+430335 b^{3} e m \,x^{8}+1291005 b^{2} c d m \,x^{8}+61 a^{3} e \,m^{6} x^{2}+183 a^{2} b d \,m^{6} x^{2}+52725 a^{2} b e \,m^{4} x^{4}+52725 a^{2} c d \,m^{4} x^{4}+1020033 a^{2} c e \,m^{2} x^{6}+52725 a \,b^{2} d \,m^{4} x^{4}+1020033 a \,b^{2} e \,m^{2} x^{6}+2040066 a b c d \,m^{2} x^{6}+1351350 a b c e \,x^{8}+675675 a \,c^{2} d \,x^{8}+340011 b^{3} d \,m^{2} x^{6}+225225 b^{3} e \,x^{8}+675675 b^{2} c d \,x^{8}+a^{3} d \,m^{7}+1525 a^{3} e \,m^{5} x^{2}+4575 a^{2} b d \,m^{5} x^{2}+360537 a^{2} b e \,m^{3} x^{4}+360537 a^{2} c d \,m^{3} x^{4}+1632285 a^{2} c e m \,x^{6}+360537 a \,b^{2} d \,m^{3} x^{4}+1632285 a \,b^{2} e m \,x^{6}+3264570 a b c d m \,x^{6}+544095 b^{3} d m \,x^{6}+63 a^{3} d \,m^{6}+20065 a^{3} e \,m^{4} x^{2}+60195 a^{2} b d \,m^{4} x^{2}+1311363 a^{2} b e \,m^{2} x^{4}+1311363 a^{2} c d \,m^{2} x^{4}+868725 a^{2} c e \,x^{6}+1311363 a \,b^{2} d \,m^{2} x^{4}+868725 a \,b^{2} e \,x^{6}+1737450 a b c d \,x^{6}+289575 b^{3} d \,x^{6}+1645 a^{3} d \,m^{5}+147859 a^{3} e \,m^{3} x^{2}+443577 a^{2} b d \,m^{3} x^{2}+2215701 a^{2} b e m \,x^{4}+2215701 a^{2} c d m \,x^{4}+2215701 a \,b^{2} d m \,x^{4}+22995 a^{3} d \,m^{4}+594439 a^{3} e \,m^{2} x^{2}+1783317 a^{2} b d \,m^{2} x^{2}+1216215 a^{2} b e \,x^{4}+1216215 a^{2} c d \,x^{4}+1216215 a \,b^{2} d \,x^{4}+185059 a^{3} d \,m^{3}+1140855 a^{3} e m \,x^{2}+3422565 a^{2} b d m \,x^{2}+852957 a^{3} d \,m^{2}+675675 a^{3} e \,x^{2}+2027025 a^{2} b d \,x^{2}+2071215 a^{3} d m +2027025 a^{3} d \right) x \left(f x \right)^{m}}{\left(m +1\right) \left(m +3\right) \left(m +5\right) \left(m +7\right) \left(m +9\right) \left(m +11\right) \left(m +13\right) \left(m +15\right)}"," ",0,"x*(c^3*e*m^7*x^14+49*c^3*e*m^6*x^14+3*b*c^2*e*m^7*x^12+c^3*d*m^7*x^12+973*c^3*e*m^5*x^14+153*b*c^2*e*m^6*x^12+51*c^3*d*m^6*x^12+10045*c^3*e*m^4*x^14+3*a*c^2*e*m^7*x^10+3*b^2*c*e*m^7*x^10+3*b*c^2*d*m^7*x^10+3135*b*c^2*e*m^5*x^12+1045*c^3*d*m^5*x^12+57379*c^3*e*m^3*x^14+159*a*c^2*e*m^6*x^10+159*b^2*c*e*m^6*x^10+159*b*c^2*d*m^6*x^10+33165*b*c^2*e*m^4*x^12+11055*c^3*d*m^4*x^12+177331*c^3*e*m^2*x^14+6*a*b*c*e*m^7*x^8+3*a*c^2*d*m^7*x^8+3375*a*c^2*e*m^5*x^10+b^3*e*m^7*x^8+3*b^2*c*d*m^7*x^8+3375*b^2*c*e*m^5*x^10+3375*b*c^2*d*m^5*x^10+193017*b*c^2*e*m^3*x^12+64339*c^3*d*m^3*x^12+264207*c^3*e*m*x^14+330*a*b*c*e*m^6*x^8+165*a*c^2*d*m^6*x^8+36795*a*c^2*e*m^4*x^10+55*b^3*e*m^6*x^8+165*b^2*c*d*m^6*x^8+36795*b^2*c*e*m^4*x^10+36795*b*c^2*d*m^4*x^10+604827*b*c^2*e*m^2*x^12+201609*c^3*d*m^2*x^12+135135*c^3*e*x^14+3*a^2*c*e*m^7*x^6+3*a*b^2*e*m^7*x^6+6*a*b*c*d*m^7*x^6+7278*a*b*c*e*m^5*x^8+3639*a*c^2*d*m^5*x^8+219417*a*c^2*e*m^3*x^10+b^3*d*m^7*x^6+1213*b^3*e*m^5*x^8+3639*b^2*c*d*m^5*x^8+219417*b^2*c*e*m^3*x^10+219417*b*c^2*d*m^3*x^10+909765*b*c^2*e*m*x^12+303255*c^3*d*m*x^12+171*a^2*c*e*m^6*x^6+171*a*b^2*e*m^6*x^6+342*a*b*c*d*m^6*x^6+82338*a*b*c*e*m^4*x^8+41169*a*c^2*d*m^4*x^8+700461*a*c^2*e*m^2*x^10+57*b^3*d*m^6*x^6+13723*b^3*e*m^4*x^8+41169*b^2*c*d*m^4*x^8+700461*b^2*c*e*m^2*x^10+700461*b*c^2*d*m^2*x^10+467775*b*c^2*e*x^12+155925*c^3*d*x^12+3*a^2*b*e*m^7*x^4+3*a^2*c*d*m^7*x^4+3927*a^2*c*e*m^5*x^6+3*a*b^2*d*m^7*x^4+3927*a*b^2*e*m^5*x^6+7854*a*b*c*d*m^5*x^6+507282*a*b*c*e*m^3*x^8+253641*a*c^2*d*m^3*x^8+1067445*a*c^2*e*m*x^10+1309*b^3*d*m^5*x^6+84547*b^3*e*m^3*x^8+253641*b^2*c*d*m^3*x^8+1067445*b^2*c*e*m*x^10+1067445*b*c^2*d*m*x^10+177*a^2*b*e*m^6*x^4+177*a^2*c*d*m^6*x^4+46431*a^2*c*e*m^4*x^6+177*a*b^2*d*m^6*x^4+46431*a*b^2*e*m^4*x^6+92862*a*b*c*d*m^4*x^6+1662558*a*b*c*e*m^2*x^8+831279*a*c^2*d*m^2*x^8+552825*a*c^2*e*x^10+15477*b^3*d*m^4*x^6+277093*b^3*e*m^2*x^8+831279*b^2*c*d*m^2*x^8+552825*b^2*c*e*x^10+552825*b*c^2*d*x^10+a^3*e*m^7*x^2+3*a^2*b*d*m^7*x^2+4239*a^2*b*e*m^5*x^4+4239*a^2*c*d*m^5*x^4+299145*a^2*c*e*m^3*x^6+4239*a*b^2*d*m^5*x^4+299145*a*b^2*e*m^3*x^6+598290*a*b*c*d*m^3*x^6+2582010*a*b*c*e*m*x^8+1291005*a*c^2*d*m*x^8+99715*b^3*d*m^3*x^6+430335*b^3*e*m*x^8+1291005*b^2*c*d*m*x^8+61*a^3*e*m^6*x^2+183*a^2*b*d*m^6*x^2+52725*a^2*b*e*m^4*x^4+52725*a^2*c*d*m^4*x^4+1020033*a^2*c*e*m^2*x^6+52725*a*b^2*d*m^4*x^4+1020033*a*b^2*e*m^2*x^6+2040066*a*b*c*d*m^2*x^6+1351350*a*b*c*e*x^8+675675*a*c^2*d*x^8+340011*b^3*d*m^2*x^6+225225*b^3*e*x^8+675675*b^2*c*d*x^8+a^3*d*m^7+1525*a^3*e*m^5*x^2+4575*a^2*b*d*m^5*x^2+360537*a^2*b*e*m^3*x^4+360537*a^2*c*d*m^3*x^4+1632285*a^2*c*e*m*x^6+360537*a*b^2*d*m^3*x^4+1632285*a*b^2*e*m*x^6+3264570*a*b*c*d*m*x^6+544095*b^3*d*m*x^6+63*a^3*d*m^6+20065*a^3*e*m^4*x^2+60195*a^2*b*d*m^4*x^2+1311363*a^2*b*e*m^2*x^4+1311363*a^2*c*d*m^2*x^4+868725*a^2*c*e*x^6+1311363*a*b^2*d*m^2*x^4+868725*a*b^2*e*x^6+1737450*a*b*c*d*x^6+289575*b^3*d*x^6+1645*a^3*d*m^5+147859*a^3*e*m^3*x^2+443577*a^2*b*d*m^3*x^2+2215701*a^2*b*e*m*x^4+2215701*a^2*c*d*m*x^4+2215701*a*b^2*d*m*x^4+22995*a^3*d*m^4+594439*a^3*e*m^2*x^2+1783317*a^2*b*d*m^2*x^2+1216215*a^2*b*e*x^4+1216215*a^2*c*d*x^4+1216215*a*b^2*d*x^4+185059*a^3*d*m^3+1140855*a^3*e*m*x^2+3422565*a^2*b*d*m*x^2+852957*a^3*d*m^2+675675*a^3*e*x^2+2027025*a^2*b*d*x^2+2071215*a^3*d*m+2027025*a^3*d)*(f*x)^m/(m+1)/(m+3)/(m+5)/(m+7)/(m+9)/(m+11)/(m+13)/(m+15)","B"
221,1,783,155,0.008000," ","int((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^2,x)","\frac{\left(c^{2} e \,m^{5} x^{10}+25 c^{2} e \,m^{4} x^{10}+2 b c e \,m^{5} x^{8}+c^{2} d \,m^{5} x^{8}+230 c^{2} e \,m^{3} x^{10}+54 b c e \,m^{4} x^{8}+27 c^{2} d \,m^{4} x^{8}+950 c^{2} e \,m^{2} x^{10}+2 a c e \,m^{5} x^{6}+b^{2} e \,m^{5} x^{6}+2 b c d \,m^{5} x^{6}+524 b c e \,m^{3} x^{8}+262 c^{2} d \,m^{3} x^{8}+1689 c^{2} e m \,x^{10}+58 a c e \,m^{4} x^{6}+29 b^{2} e \,m^{4} x^{6}+58 b c d \,m^{4} x^{6}+2244 b c e \,m^{2} x^{8}+1122 c^{2} d \,m^{2} x^{8}+945 e \,c^{2} x^{10}+2 a b e \,m^{5} x^{4}+2 a c d \,m^{5} x^{4}+604 a c e \,m^{3} x^{6}+b^{2} d \,m^{5} x^{4}+302 b^{2} e \,m^{3} x^{6}+604 b c d \,m^{3} x^{6}+4082 b c e m \,x^{8}+2041 c^{2} d m \,x^{8}+62 a b e \,m^{4} x^{4}+62 a c d \,m^{4} x^{4}+2732 a c e \,m^{2} x^{6}+31 b^{2} d \,m^{4} x^{4}+1366 b^{2} e \,m^{2} x^{6}+2732 b c d \,m^{2} x^{6}+2310 b c e \,x^{8}+1155 c^{2} d \,x^{8}+a^{2} e \,m^{5} x^{2}+2 a b d \,m^{5} x^{2}+700 a b e \,m^{3} x^{4}+700 a c d \,m^{3} x^{4}+5154 a c e m \,x^{6}+350 b^{2} d \,m^{3} x^{4}+2577 b^{2} e m \,x^{6}+5154 b c d m \,x^{6}+33 a^{2} e \,m^{4} x^{2}+66 a b d \,m^{4} x^{2}+3460 a b e \,m^{2} x^{4}+3460 a c d \,m^{2} x^{4}+2970 a c e \,x^{6}+1730 b^{2} d \,m^{2} x^{4}+1485 b^{2} e \,x^{6}+2970 b c d \,x^{6}+a^{2} d \,m^{5}+406 a^{2} e \,m^{3} x^{2}+812 a b d \,m^{3} x^{2}+6978 a b e m \,x^{4}+6978 a c d m \,x^{4}+3489 b^{2} d m \,x^{4}+35 a^{2} d \,m^{4}+2262 a^{2} e \,m^{2} x^{2}+4524 a b d \,m^{2} x^{2}+4158 a b e \,x^{4}+4158 a c d \,x^{4}+2079 b^{2} d \,x^{4}+470 a^{2} d \,m^{3}+5353 a^{2} e m \,x^{2}+10706 a b d m \,x^{2}+3010 a^{2} d \,m^{2}+3465 a^{2} e \,x^{2}+6930 a b d \,x^{2}+9129 a^{2} d m +10395 d \,a^{2}\right) x \left(f x \right)^{m}}{\left(m +11\right) \left(m +9\right) \left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"x*(c^2*e*m^5*x^10+25*c^2*e*m^4*x^10+2*b*c*e*m^5*x^8+c^2*d*m^5*x^8+230*c^2*e*m^3*x^10+54*b*c*e*m^4*x^8+27*c^2*d*m^4*x^8+950*c^2*e*m^2*x^10+2*a*c*e*m^5*x^6+b^2*e*m^5*x^6+2*b*c*d*m^5*x^6+524*b*c*e*m^3*x^8+262*c^2*d*m^3*x^8+1689*c^2*e*m*x^10+58*a*c*e*m^4*x^6+29*b^2*e*m^4*x^6+58*b*c*d*m^4*x^6+2244*b*c*e*m^2*x^8+1122*c^2*d*m^2*x^8+945*c^2*e*x^10+2*a*b*e*m^5*x^4+2*a*c*d*m^5*x^4+604*a*c*e*m^3*x^6+b^2*d*m^5*x^4+302*b^2*e*m^3*x^6+604*b*c*d*m^3*x^6+4082*b*c*e*m*x^8+2041*c^2*d*m*x^8+62*a*b*e*m^4*x^4+62*a*c*d*m^4*x^4+2732*a*c*e*m^2*x^6+31*b^2*d*m^4*x^4+1366*b^2*e*m^2*x^6+2732*b*c*d*m^2*x^6+2310*b*c*e*x^8+1155*c^2*d*x^8+a^2*e*m^5*x^2+2*a*b*d*m^5*x^2+700*a*b*e*m^3*x^4+700*a*c*d*m^3*x^4+5154*a*c*e*m*x^6+350*b^2*d*m^3*x^4+2577*b^2*e*m*x^6+5154*b*c*d*m*x^6+33*a^2*e*m^4*x^2+66*a*b*d*m^4*x^2+3460*a*b*e*m^2*x^4+3460*a*c*d*m^2*x^4+2970*a*c*e*x^6+1730*b^2*d*m^2*x^4+1485*b^2*e*x^6+2970*b*c*d*x^6+a^2*d*m^5+406*a^2*e*m^3*x^2+812*a*b*d*m^3*x^2+6978*a*b*e*m*x^4+6978*a*c*d*m*x^4+3489*b^2*d*m*x^4+35*a^2*d*m^4+2262*a^2*e*m^2*x^2+4524*a*b*d*m^2*x^2+4158*a*b*e*x^4+4158*a*c*d*x^4+2079*b^2*d*x^4+470*a^2*d*m^3+5353*a^2*e*m*x^2+10706*a*b*d*m*x^2+3010*a^2*d*m^2+3465*a^2*e*x^2+6930*a*b*d*x^2+9129*a^2*d*m+10395*a^2*d)*(f*x)^m/(m+11)/(m+9)/(m+7)/(m+5)/(m+3)/(m+1)","B"
222,1,221,83,0.004000," ","int((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a),x)","\frac{\left(c e \,m^{3} x^{6}+9 c e \,m^{2} x^{6}+b e \,m^{3} x^{4}+c d \,m^{3} x^{4}+23 c e m \,x^{6}+11 b e \,m^{2} x^{4}+11 c d \,m^{2} x^{4}+15 c e \,x^{6}+a e \,m^{3} x^{2}+b d \,m^{3} x^{2}+31 b e m \,x^{4}+31 c d m \,x^{4}+13 a e \,m^{2} x^{2}+13 b d \,m^{2} x^{2}+21 b e \,x^{4}+21 c d \,x^{4}+a d \,m^{3}+47 a e m \,x^{2}+47 b d m \,x^{2}+15 a d \,m^{2}+35 a e \,x^{2}+35 b d \,x^{2}+71 a d m +105 a d \right) x \left(f x \right)^{m}}{\left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"x*(c*e*m^3*x^6+9*c*e*m^2*x^6+b*e*m^3*x^4+c*d*m^3*x^4+23*c*e*m*x^6+11*b*e*m^2*x^4+11*c*d*m^2*x^4+15*c*e*x^6+a*e*m^3*x^2+b*d*m^3*x^2+31*b*e*m*x^4+31*c*d*m*x^4+13*a*e*m^2*x^2+13*b*d*m^2*x^2+21*b*e*x^4+21*c*d*x^4+a*d*m^3+47*a*e*m*x^2+47*b*d*m*x^2+15*a*d*m^2+35*a*e*x^2+35*b*d*x^2+71*a*d*m+105*a*d)*(f*x)^m/(m+7)/(m+5)/(m+3)/(m+1)","B"
223,0,0,176,0.037000," ","int((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a),x)","\int \frac{\left(e \,x^{2}+d \right) \left(f x \right)^{m}}{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a),x)","F"
224,0,0,362,0.028000," ","int((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","\int \frac{\left(e \,x^{2}+d \right) \left(f x \right)^{m}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}\, dx"," ",0,"int((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a)^2,x)","F"
225,0,0,275,0.012000," ","int((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^(3/2),x)","\int \left(e \,x^{2}+d \right) \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} \left(f x \right)^{m}\, dx"," ",0,"int((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^(3/2),x)","F"
226,0,0,273,0.011000," ","int((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^(1/2),x)","\int \left(e \,x^{2}+d \right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(f x \right)^{m}\, dx"," ",0,"int((f*x)^m*(e*x^2+d)*(c*x^4+b*x^2+a)^(1/2),x)","F"
227,0,0,273,0.014000," ","int((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","\int \frac{\left(e \,x^{2}+d \right) \left(f x \right)^{m}}{\sqrt{c \,x^{4}+b \,x^{2}+a}}\, dx"," ",0,"int((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","F"
228,0,0,279,0.012000," ","int((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","\int \frac{\left(e \,x^{2}+d \right) \left(f x \right)^{m}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((f*x)^m*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","F"
229,1,122,116,0.014000," ","int(x^9/(e*x^2+d)/(c*x^4+a),x)","\frac{a^{2} d \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{a c}\, c}-\frac{a^{2} e \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right) c^{2}}+\frac{x^{4}}{4 c e}+\frac{d^{4} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right) e^{3}}-\frac{d \,x^{2}}{2 c \,e^{2}}"," ",0,"1/4*x^4/c/e-1/2*d*x^2/c/e^2-1/4*a^2*e*ln(c*x^4+a)/c^2/(a*e^2+c*d^2)+1/2*a^2/(a*e^2+c*d^2)/c*d/(a*c)^(1/2)*arctan(c*x^2/(a*c)^(1/2))+1/2*d^4*ln(e*x^2+d)/e^3/(a*e^2+c*d^2)","A"
230,1,108,102,0.010000," ","int(x^7/(e*x^2+d)/(c*x^4+a),x)","-\frac{a^{2} e \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{a c}\, c}-\frac{a d \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right) c}-\frac{d^{3} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right) e^{2}}+\frac{x^{2}}{2 c e}"," ",0,"1/2*x^2/c/e-1/4*a*d*ln(c*x^4+a)/c/(a*e^2+c*d^2)-1/2*a^2/(a*e^2+c*d^2)/c*e/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)-1/2*d^3*ln(e*x^2+d)/e^2/(a*e^2+c*d^2)","A"
231,1,92,91,0.009000," ","int(x^5/(e*x^2+d)/(c*x^4+a),x)","-\frac{a d \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{a c}}+\frac{a e \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right) c}+\frac{d^{2} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right) e}"," ",0,"1/4*a*e*ln(c*x^4+a)/c/(a*e^2+c*d^2)-1/2*a/(a*e^2+c*d^2)*d/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)+1/2*d^2*ln(e*x^2+d)/e/(a*e^2+c*d^2)","A"
232,1,83,82,0.007000," ","int(x^3/(e*x^2+d)/(c*x^4+a),x)","\frac{a e \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{a c}}+\frac{d \ln \left(c \,x^{4}+a \right)}{4 a \,e^{2}+4 c \,d^{2}}-\frac{d \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)}"," ",0,"1/4*d*ln(c*x^4+a)/(a*e^2+c*d^2)+1/2/(a*e^2+c*d^2)*a*e/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)-1/2*d*ln(e*x^2+d)/(a*e^2+c*d^2)","A"
233,1,83,82,0.007000," ","int(x/(e*x^2+d)/(c*x^4+a),x)","\frac{c d \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{a c}}-\frac{e \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right)}+\frac{e \ln \left(e \,x^{2}+d \right)}{2 a \,e^{2}+2 c \,d^{2}}"," ",0,"-1/4*e*ln(c*x^4+a)/(a*e^2+c*d^2)+1/2*c/(a*e^2+c*d^2)*d/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)+1/2*e*ln(e*x^2+d)/(a*e^2+c*d^2)","A"
234,1,101,100,0.010000," ","int(1/x/(e*x^2+d)/(c*x^4+a),x)","-\frac{c e \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{a c}}-\frac{c d \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right) a}-\frac{e^{2} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right) d}+\frac{\ln \left(x \right)}{a d}"," ",0,"ln(x)/a/d-1/4*c*d*ln(c*x^4+a)/a/(a*e^2+c*d^2)-1/2*c/(a*e^2+c*d^2)*e/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)-1/2*e^2*ln(e*x^2+d)/d/(a*e^2+c*d^2)","A"
235,1,119,113,0.013000," ","int(1/x^3/(e*x^2+d)/(c*x^4+a),x)","-\frac{c^{2} d \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{a c}\, a}+\frac{c e \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right) a}+\frac{e^{3} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right) d^{2}}-\frac{e \ln \left(x \right)}{a \,d^{2}}-\frac{1}{2 a d \,x^{2}}"," ",0,"-1/2/a/d/x^2-e*ln(x)/a/d^2+1/4*c*e*ln(c*x^4+a)/a/(a*e^2+c*d^2)-1/2*c^2/(a*e^2+c*d^2)/a*d/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)+1/2*e^3*ln(e*x^2+d)/d^2/(a*e^2+c*d^2)","A"
236,1,145,138,0.016000," ","int(1/x^5/(e*x^2+d)/(c*x^4+a),x)","\frac{c^{2} e \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{a c}\, a}+\frac{c^{2} d \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right) a^{2}}-\frac{e^{4} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right) d^{3}}+\frac{e^{2} \ln \left(x \right)}{a \,d^{3}}-\frac{c \ln \left(x \right)}{a^{2} d}+\frac{e}{2 a \,d^{2} x^{2}}-\frac{1}{4 a d \,x^{4}}"," ",0,"-1/4/a/d/x^4+1/d^3/a*ln(x)*e^2-1/d/a^2*ln(x)*c+1/2*e/a/d^2/x^2+1/4*c^2*d*ln(c*x^4+a)/a^2/(a*e^2+c*d^2)+1/2*c^2/(a*e^2+c*d^2)/a*e/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)-1/2*e^4*ln(e*x^2+d)/d^3/(a*e^2+c*d^2)","A"
237,1,405,268,0.017000," ","int(x^8/(e*x^2+d)/(c*x^4+a),x)","\frac{d^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{d e}\, e^{2}}-\frac{\sqrt{2}\, a^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}-\frac{\sqrt{2}\, a^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}-\frac{\sqrt{2}\, a^{2} e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) c}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) c}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a d \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) c}+\frac{x^{3}}{3 c e}-\frac{d x}{c \,e^{2}}"," ",0,"1/3*x^3/c/e-d*x/c/e^2+1/8*a/(a*e^2+c*d^2)/c*d*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2)))+1/4*a/(a*e^2+c*d^2)/c*d*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+1/4*a/(a*e^2+c*d^2)/c*d*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)-1/8*a^2/(a*e^2+c*d^2)/c^2*e/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*x*2^(1/2)+(a/c)^(1/2)))-1/4*a^2/(a*e^2+c*d^2)/c^2*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)-1/4*a^2/(a*e^2+c*d^2)/c^2*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)+1/e^2*d^4/(a*e^2+c*d^2)/(d*e)^(1/2)*arctan(e*x/(d*e)^(1/2))","A"
238,1,387,256,0.008000," ","int(x^6/(e*x^2+d)/(c*x^4+a),x)","-\frac{d^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{d e}\, e}-\frac{\sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, a d \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} c}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) c}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) c}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a e \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) c}+\frac{x}{c e}"," ",0,"x/c/e-1/4*a/(a*e^2+c*d^2)/c*e*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)-1/8*a/(a*e^2+c*d^2)/c*e*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))-1/4*a/(a*e^2+c*d^2)/c*e*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)-1/8*a/(a*e^2+c*d^2)/c*d/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))-1/4*a/(a*e^2+c*d^2)/c*d/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)-1/4*a/(a*e^2+c*d^2)/c*d/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)-1/e*d^3/(a*e^2+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","A"
239,1,363,247,0.009000," ","int(x^4/(e*x^2+d)/(c*x^4+a),x)","\frac{d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{d e}}+\frac{\sqrt{2}\, a e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, a e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, a e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} c}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)}"," ",0,"-1/8/(a*e^2+c*d^2)*d*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))-1/4/(a*e^2+c*d^2)*d*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)-1/4/(a*e^2+c*d^2)*d*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)+1/8*a/(a*e^2+c*d^2)*e/c/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+1/4*a/(a*e^2+c*d^2)*e/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+1/4*a/(a*e^2+c*d^2)*e/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)+d^2/(a*e^2+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","A"
240,1,351,248,0.009000," ","int(x^2/(e*x^2+d)/(c*x^4+a),x)","-\frac{d e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{d e}}+\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}}}+\frac{\sqrt{2}\, d \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}}}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 a \,e^{2}+4 c \,d^{2}}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 a \,e^{2}+4 c \,d^{2}}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, e \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 a \,e^{2}+8 c \,d^{2}}"," ",0,"1/4/(a*e^2+c*d^2)*e*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)+1/8/(a*e^2+c*d^2)*e*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+1/4/(a*e^2+c*d^2)*e*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+1/8/(a*e^2+c*d^2)*d/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+1/4/(a*e^2+c*d^2)*d/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+1/4/(a*e^2+c*d^2)*d/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)-d*e/(a*e^2+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","A"
241,1,363,247,0.008000," ","int(1/(e*x^2+d)/(c*x^4+a),x)","\frac{e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{d e}}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c d \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) a}-\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}}}"," ",0,"1/8*c/(a*e^2+c*d^2)*d*(a/c)^(1/4)/a*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+1/4*c/(a*e^2+c*d^2)*d*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+1/4*c/(a*e^2+c*d^2)*d*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)-1/8/(a*e^2+c*d^2)*e/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))-1/4/(a*e^2+c*d^2)*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)-1/4/(a*e^2+c*d^2)*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)+e^2/(a*e^2+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","A"
242,1,390,259,0.012000," ","int(1/x^2/(e*x^2+d)/(c*x^4+a),x)","-\frac{e^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{d e}\, d}-\frac{\sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, c d \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) a}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) a}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c e \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) a}-\frac{1}{a d x}"," ",0,"-1/a/d/x-1/4*c/(a*e^2+c*d^2)/a*e*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)-1/8*c/(a*e^2+c*d^2)/a*e*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))-1/4*c/(a*e^2+c*d^2)/a*e*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)-1/8*c/(a*e^2+c*d^2)/a*d/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))-1/4*c/(a*e^2+c*d^2)/a*d/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)-1/4*c/(a*e^2+c*d^2)/a*d/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)-1/d*e^3/(a*e^2+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","A"
243,1,406,269,0.012000," ","int(1/x^4/(e*x^2+d)/(c*x^4+a),x)","\frac{e^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{d e}\, d^{2}}+\frac{\sqrt{2}\, c e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, c e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, c e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) a^{2}}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a \,e^{2}+c \,d^{2}\right) a^{2}}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right) a^{2}}+\frac{e}{a \,d^{2} x}-\frac{1}{3 a d \,x^{3}}"," ",0,"-1/3/a/d/x^3+e/a/d^2/x-1/8*c^2/(a*e^2+c*d^2)/a^2*d*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))-1/4*c^2/(a*e^2+c*d^2)/a^2*d*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)-1/4*c^2/(a*e^2+c*d^2)/a^2*d*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)+1/8*c/(a*e^2+c*d^2)/a*e/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))+1/4*c/(a*e^2+c*d^2)/a*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)+1/4*c/(a*e^2+c*d^2)/a*e/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)+1/d^2*e^4/(a*e^2+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","A"
244,1,305,153,0.020000," ","int(x^9/(e*x^2+d)/(c*x^4+a)^2,x)","\frac{a^{2} d \,e^{2} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) c}+\frac{a \,d^{3} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{a^{2} d \,e^{2} \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}\, c}-\frac{3 a \,d^{3} \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}}+\frac{a^{3} e^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) c^{2}}+\frac{a^{2} d^{2} e}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) c}+\frac{a^{2} e^{3} \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} c^{2}}+\frac{a \,d^{2} e \ln \left(c \,x^{4}+a \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} c}+\frac{d^{4} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} e}"," ",0,"1/4*a^2/(a*e^2+c*d^2)^2/(c*x^4+a)*d/c*x^2*e^2+1/4*a/(a*e^2+c*d^2)^2/(c*x^4+a)*x^2*d^3+1/4*a^3/(a*e^2+c*d^2)^2/(c*x^4+a)*e^3/c^2+1/4*a^2/(a*e^2+c*d^2)^2/(c*x^4+a)*e/c*d^2+1/4*a^2/(a*e^2+c*d^2)^2/c^2*ln(c*x^4+a)*e^3+1/2*a/(a*e^2+c*d^2)^2/c*ln(c*x^4+a)*d^2*e-1/4*a^2/(a*e^2+c*d^2)^2/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*d*e^2-3/4*a/(a*e^2+c*d^2)^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*d^3+1/2*d^4*ln(e*x^2+d)/e/(a*e^2+c*d^2)^2","A"
245,1,260,134,0.019000," ","int(x^7/(e*x^2+d)/(c*x^4+a)^2,x)","-\frac{a^{2} e^{3} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) c}-\frac{a \,d^{2} e \,x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{a^{2} e^{3} \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}\, c}+\frac{3 a \,d^{2} e \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}}+\frac{a^{2} d \,e^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) c}+\frac{a \,d^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{d^{3} \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2}}-\frac{d^{3} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2}}"," ",0,"-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*a^2*e^3/c*x^2-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*a*e*x^2*d^2+1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*a^2*d/c*e^2+1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*a*d^3+1/4*d^3*ln(c*x^4+a)/(a*e^2+c*d^2)^2+1/4/(a*e^2+c*d^2)^2/c/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*a^2*e^3+3/4/(a*e^2+c*d^2)^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*a*d^2*e-1/2*d^3*ln(e*x^2+d)/(a*e^2+c*d^2)^2","A"
246,1,252,139,0.016000," ","int(x^5/(e*x^2+d)/(c*x^4+a)^2,x)","-\frac{a d \,e^{2} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{c \,d^{3} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{a d \,e^{2} \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}}+\frac{c \,d^{3} \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}}-\frac{a^{2} e^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) c}-\frac{a \,d^{2} e}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{d^{2} e \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2}}+\frac{d^{2} e \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2}}"," ",0,"-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*x^2*a*d*e^2-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*x^2*c*d^3-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*a^2*e^3/c-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*a*e*d^2-1/4*d^2*e*ln(c*x^4+a)/(a*e^2+c*d^2)^2-1/4/(a*e^2+c*d^2)^2*d/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*a*e^2+1/4/(a*e^2+c*d^2)^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*c*d^3+1/2*d^2*e*ln(e*x^2+d)/(a*e^2+c*d^2)^2","A"
247,1,247,133,0.015000," ","int(x^3/(e*x^2+d)/(c*x^4+a)^2,x)","\frac{a \,e^{3} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{c \,d^{2} e \,x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{a \,e^{3} \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}}-\frac{c \,d^{2} e \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}}-\frac{a d \,e^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{c \,d^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{d \,e^{2} \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2}}-\frac{d \,e^{2} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2}}"," ",0,"1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*x^2*e^3*a+1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*x^2*e*c*d^2-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*a*d*e^2-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*c*d^3+1/4*d*e^2*ln(c*x^4+a)/(a*e^2+c*d^2)^2+1/4/(a*e^2+c*d^2)^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*a*e^3-1/4/(a*e^2+c*d^2)^2*e/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*c*d^2-1/2*d*e^2*ln(e*x^2+d)/(a*e^2+c*d^2)^2","A"
248,1,255,135,0.017000," ","int(x/(e*x^2+d)/(c*x^4+a)^2,x)","\frac{c^{2} d^{3} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}+\frac{c d \,e^{2} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{c^{2} d^{3} \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}\, a}+\frac{3 c d \,e^{2} \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}}+\frac{a \,e^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{c \,d^{2} e}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{e^{3} \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2}}+\frac{e^{3} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2}}"," ",0,"1/4*c/(a*e^2+c*d^2)^2/(c*x^4+a)*d*x^2*e^2+1/4*c^2/(a*e^2+c*d^2)^2/(c*x^4+a)*d^3/a*x^2+1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*e^3*a+1/4*c/(a*e^2+c*d^2)^2/(c*x^4+a)*e*d^2-1/4*e^3*ln(c*x^4+a)/(a*e^2+c*d^2)^2+3/4*c/(a*e^2+c*d^2)^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*d*e^2+1/4*c^2/(a*e^2+c*d^2)^2/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*d^3+1/2*e^3*ln(e*x^2+d)/(a*e^2+c*d^2)^2","A"
249,1,309,183,0.023000," ","int(1/x/(e*x^2+d)/(c*x^4+a)^2,x)","-\frac{c^{2} d^{2} e \,x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}-\frac{c \,e^{3} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{c^{2} d^{2} e \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}\, a}-\frac{3 c \,e^{3} \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}}+\frac{c^{2} d^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}-\frac{c d \,e^{2} \ln \left(c \,x^{4}+a \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}-\frac{c^{2} d^{3} \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}+\frac{c d \,e^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{e^{4} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} d}+\frac{\ln \left(x \right)}{a^{2} d}"," ",0,"ln(x)/a^2/d-1/4*c/(a*e^2+c*d^2)^2/(c*x^4+a)*e^3*x^2-1/4*c^2/(a*e^2+c*d^2)^2/a/(c*x^4+a)*x^2*e*d^2+1/4*c/(a*e^2+c*d^2)^2/(c*x^4+a)*d*e^2+1/4*c^2/(a*e^2+c*d^2)^2/a/(c*x^4+a)*d^3-1/2*c/(a*e^2+c*d^2)^2/a*ln(c*x^4+a)*d*e^2-1/4*c^2/(a*e^2+c*d^2)^2/a^2*ln(c*x^4+a)*d^3-3/4*c/(a*e^2+c*d^2)^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*e^3-1/4*c^2/(a*e^2+c*d^2)^2/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*e*d^2-1/2*e^4*ln(e*x^2+d)/d/(a*e^2+c*d^2)^2","A"
250,1,332,208,0.025000," ","int(1/x^3/(e*x^2+d)/(c*x^4+a)^2,x)","-\frac{c^{2} d \,e^{2} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}-\frac{c^{3} d^{3} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a^{2}}-\frac{5 c^{2} d \,e^{2} \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}\, a}-\frac{3 c^{3} d^{3} \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}\, a^{2}}-\frac{c^{2} d^{2} e}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}+\frac{c \,e^{3} \ln \left(c \,x^{4}+a \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{c^{2} d^{2} e \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}-\frac{c \,e^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{e^{5} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} d^{2}}-\frac{e \ln \left(x \right)}{a^{2} d^{2}}-\frac{1}{2 a^{2} d \,x^{2}}"," ",0,"-1/2/a^2/d/x^2-e*ln(x)/a^2/d^2-1/4*c^2/(a*e^2+c*d^2)^2/a/(c*x^4+a)*x^2*d*e^2-1/4*c^3/(a*e^2+c*d^2)^2/a^2/(c*x^4+a)*x^2*d^3-1/4*c/(a*e^2+c*d^2)^2/(c*x^4+a)*e^3-1/4*c^2/(a*e^2+c*d^2)^2/a/(c*x^4+a)*e*d^2+1/2*c/(a*e^2+c*d^2)^2/a*ln(c*x^4+a)*e^3+1/4*c^2/(a*e^2+c*d^2)^2/a^2*ln(c*x^4+a)*e*d^2-5/4*c^2/(a*e^2+c*d^2)^2/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*d*e^2-3/4*c^3/(a*e^2+c*d^2)^2/a^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*d^3+1/2*e^5*ln(e*x^2+d)/d^2/(a*e^2+c*d^2)^2","A"
251,1,363,235,0.025000," ","int(1/x^5/(e*x^2+d)/(c*x^4+a)^2,x)","\frac{c^{2} e^{3} x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}+\frac{c^{3} d^{2} e \,x^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a^{2}}+\frac{5 c^{2} e^{3} \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}\, a}+\frac{3 c^{3} d^{2} e \arctan \left(\frac{c \,x^{2}}{\sqrt{a c}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a c}\, a^{2}}-\frac{c^{2} d \,e^{2}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}-\frac{c^{3} d^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a^{2}}+\frac{3 c^{2} d \,e^{2} \ln \left(c \,x^{4}+a \right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}+\frac{c^{3} d^{3} \ln \left(c \,x^{4}+a \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{3}}-\frac{e^{6} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} d^{3}}+\frac{e^{2} \ln \left(x \right)}{a^{2} d^{3}}-\frac{2 c \ln \left(x \right)}{a^{3} d}+\frac{e}{2 a^{2} d^{2} x^{2}}-\frac{1}{4 a^{2} d \,x^{4}}"," ",0,"-1/4/a^2/d/x^4+1/a^2/d^3*ln(x)*e^2-2/a^3/d*ln(x)*c+1/2*e/a^2/d^2/x^2+1/4*c^2/(a*e^2+c*d^2)^2/a/(c*x^4+a)*e^3*x^2+1/4*c^3/(a*e^2+c*d^2)^2/a^2/(c*x^4+a)*x^2*e*d^2-1/4*c^2/(a*e^2+c*d^2)^2/a/(c*x^4+a)*d*e^2-1/4*c^3/(a*e^2+c*d^2)^2/a^2/(c*x^4+a)*d^3+3/4*c^2/(a*e^2+c*d^2)^2/a^2*ln(c*x^4+a)*d*e^2+1/2*c^3/(a*e^2+c*d^2)^2/a^3*ln(c*x^4+a)*d^3+5/4*c^2/(a*e^2+c*d^2)^2/a/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*e^3+3/4*c^3/(a*e^2+c*d^2)^2/a^2/(a*c)^(1/2)*arctan(1/(a*c)^(1/2)*c*x^2)*e*d^2-1/2*e^6*ln(e*x^2+d)/d^3/(a*e^2+c*d^2)^2","A"
252,1,873,538,0.017000," ","int(x^8/(e*x^2+d)/(c*x^4+a)^2,x)","-\frac{a^{2} e^{3} x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) c}-\frac{a \,d^{2} e \,x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{a^{2} d \,e^{2} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) c}+\frac{a \,d^{3} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{d^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{d e}}+\frac{3 \sqrt{2}\, a^{2} e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}+\frac{3 \sqrt{2}\, a^{2} e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}+\frac{3 \sqrt{2}\, a^{2} e^{3} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} c^{2}}+\frac{7 \sqrt{2}\, a \,d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{7 \sqrt{2}\, a \,d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{7 \sqrt{2}\, a \,d^{2} e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} c}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} c}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} c}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a d \,e^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} c}-\frac{5 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2}}-\frac{5 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2}}-\frac{5 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2}}"," ",0,"-1/4*a^2/(a*e^2+c*d^2)^2/(c*x^4+a)*e^3/c*x^3-1/4*a/(a*e^2+c*d^2)^2/(c*x^4+a)*e*x^3*d^2+1/4*a^2/(a*e^2+c*d^2)^2/(c*x^4+a)*d/c*x*e^2+1/4*a/(a*e^2+c*d^2)^2/(c*x^4+a)*d^3*x-1/16*a/(a*e^2+c*d^2)^2/c*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d*e^2-5/16/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^3-1/32*a/(a*e^2+c*d^2)^2/c*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d*e^2-5/32/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^3-1/16*a/(a*e^2+c*d^2)^2/c*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d*e^2-5/16/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^3+3/32*a^2/(a*e^2+c*d^2)^2/c^2/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*e^3+7/32*a/(a*e^2+c*d^2)^2/c/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^2*e+3/16*a^2/(a*e^2+c*d^2)^2/c^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*e^3+7/16*a/(a*e^2+c*d^2)^2/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2*e+3/16*a^2/(a*e^2+c*d^2)^2/c^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*e^3+7/16*a/(a*e^2+c*d^2)^2/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2*e+d^4/(a*e^2+c*d^2)^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","A"
253,1,852,515,0.019000," ","int(x^6/(e*x^2+d)/(c*x^4+a)^2,x)","-\frac{a d \,e^{2} x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{c \,d^{3} x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{a^{2} e^{3} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) c}-\frac{a \,d^{2} e x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{d^{3} e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{d e}}-\frac{\sqrt{2}\, a d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, a d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} c}-\frac{\sqrt{2}\, a d \,e^{2} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} c}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} c}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, a \,e^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} c}+\frac{3 \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}+\frac{3 \sqrt{2}\, d^{3} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}+\frac{5 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2}}+\frac{5 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2}}+\frac{5 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} e \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2}}"," ",0,"-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*x^3*a*d*e^2-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*x^3*c*d^3-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*a^2*e^3/c*x-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*e*a*d^2*x+1/16/(a*e^2+c*d^2)^2/c*(a/c)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*e^3+5/16/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2*e+1/32/(a*e^2+c*d^2)^2/c*(a/c)^(1/4)*a*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*e^3+5/32/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^2*e+1/16/(a*e^2+c*d^2)^2/c*(a/c)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*e^3+5/16/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2*e-1/32/(a*e^2+c*d^2)^2/c/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*a*d*e^2+3/32/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^3-1/16/(a*e^2+c*d^2)^2/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*a*d*e^2+3/16/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^3-1/16/(a*e^2+c*d^2)^2/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*a*d*e^2+3/16/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^3-d^3*e/(a*e^2+c*d^2)^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","A"
254,1,848,513,0.016000," ","int(x^4/(e*x^2+d)/(c*x^4+a)^2,x)","\frac{a \,e^{3} x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{c \,d^{2} e \,x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{a d \,e^{2} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{c \,d^{3} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{d^{2} e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{d e}}+\frac{\sqrt{2}\, a \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, a \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, a \,e^{3} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} c}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}-\frac{3 \sqrt{2}\, d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{3 \sqrt{2}\, d^{2} e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2}}-\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2}}-\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, d \,e^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2}}"," ",0,"1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*x^3*e^3*a+1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*x^3*e*c*d^2-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*x*a*d*e^2-1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*x*c*d^3-3/16/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d*e^2+1/16/(a*e^2+c*d^2)^2*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*c*d^3-3/32/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d*e^2+1/32/(a*e^2+c*d^2)^2*(a/c)^(1/4)/a*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*c*d^3-3/16/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d*e^2+1/16/(a*e^2+c*d^2)^2*(a/c)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*c*d^3+1/32/(a*e^2+c*d^2)^2/c/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*a*e^3-3/32/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^2*e+1/16/(a*e^2+c*d^2)^2/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*a*e^3-3/16/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2*e+1/16/(a*e^2+c*d^2)^2/c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*a*e^3-3/16/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2*e+e^2/(a*e^2+c*d^2)^2*d^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","A"
255,1,852,513,0.017000," ","int(x^2/(e*x^2+d)/(c*x^4+a)^2,x)","\frac{c^{2} d^{3} x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}+\frac{c d \,e^{2} x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{a \,e^{3} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{c \,d^{2} e x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{d \,e^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{d e}}+\frac{\sqrt{2}\, c \,d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, c \,d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}+\frac{\sqrt{2}\, c \,d^{3} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}-\frac{\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} e \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{5 \sqrt{2}\, d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}+\frac{5 \sqrt{2}\, d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}+\frac{5 \sqrt{2}\, d \,e^{2} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, e^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2}}"," ",0,"1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*c*d*x^3*e^2+1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*c^2*d^3/a*x^3+1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*x*e^3*a+1/4/(a*e^2+c*d^2)^2/(c*x^4+a)*x*e*c*d^2+3/16/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*e^3-1/16/(a*e^2+c*d^2)^2/a*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*c*d^2*e+3/32/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*e^3-1/32/(a*e^2+c*d^2)^2/a*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*c*d^2*e+3/16/(a*e^2+c*d^2)^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*e^3-1/16/(a*e^2+c*d^2)^2/a*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*c*d^2*e+5/32/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d*e^2+1/32/(a*e^2+c*d^2)^2/a*c/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^3+5/16/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d*e^2+1/16/(a*e^2+c*d^2)^2/a*c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^3+5/16/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d*e^2+1/16/(a*e^2+c*d^2)^2/a*c/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^3-d*e^3/(a*e^2+c*d^2)^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","A"
256,1,873,517,0.018000," ","int(1/(e*x^2+d)/(c*x^4+a)^2,x)","-\frac{c^{2} d^{2} e \,x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}-\frac{c \,e^{3} x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{c^{2} d^{3} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}+\frac{c d \,e^{2} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}+\frac{e^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{d e}}-\frac{\sqrt{2}\, c \,d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, c \,d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{\sqrt{2}\, c \,d^{2} e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}+\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c d \,e^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}+\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}-\frac{5 \sqrt{2}\, e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{5 \sqrt{2}\, e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}-\frac{5 \sqrt{2}\, e^{3} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}}}"," ",0,"-1/4*c/(a*e^2+c*d^2)^2/(c*x^4+a)*e^3*x^3-1/4*c^2/(a*e^2+c*d^2)^2/(c*x^4+a)*e/a*x^3*d^2+1/4*c/(a*e^2+c*d^2)^2/(c*x^4+a)*d*x*e^2+1/4*c^2/(a*e^2+c*d^2)^2/(c*x^4+a)*d^3/a*x+7/16*c/(a*e^2+c*d^2)^2/a*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d*e^2+3/16*c^2/(a*e^2+c*d^2)^2/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^3+7/32*c/(a*e^2+c*d^2)^2/a*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d*e^2+3/32*c^2/(a*e^2+c*d^2)^2/a^2*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^3+7/16*c/(a*e^2+c*d^2)^2/a*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d*e^2+3/16*c^2/(a*e^2+c*d^2)^2/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^3-5/32/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*e^3-1/32*c/(a*e^2+c*d^2)^2/a/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^2*e-5/16/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*e^3-1/16*c/(a*e^2+c*d^2)^2/a/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2*e-5/16/(a*e^2+c*d^2)^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*e^3-1/16*c/(a*e^2+c*d^2)^2/a/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2*e+e^4/(a*e^2+c*d^2)^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","A"
257,1,911,573,0.020000," ","int(1/x^2/(e*x^2+d)/(c*x^4+a)^2,x)","-\frac{c^{2} d \,e^{2} x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}-\frac{c^{3} d^{3} x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a^{2}}-\frac{c^{2} d^{2} e x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}-\frac{c \,e^{3} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right)}-\frac{e^{5} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{d e}\, d}-\frac{9 \sqrt{2}\, c d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{9 \sqrt{2}\, c d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{9 \sqrt{2}\, c d \,e^{2} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}-\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}-\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}-\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \,e^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}-\frac{5 \sqrt{2}\, c^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a^{2}}-\frac{5 \sqrt{2}\, c^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a^{2}}-\frac{5 \sqrt{2}\, c^{2} d^{3} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a^{2}}-\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}-\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}-\frac{3 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{2} e \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}-\frac{1}{a^{2} d x}"," ",0,"-1/a^2/d/x-1/4*c^2/(a*e^2+c*d^2)^2/a/(c*x^4+a)*x^3*d*e^2-1/4*c^3/(a*e^2+c*d^2)^2/a^2/(c*x^4+a)*x^3*d^3-1/4*c/(a*e^2+c*d^2)^2/(c*x^4+a)*x*e^3-1/4*c^2/(a*e^2+c*d^2)^2/a/(c*x^4+a)*x*e*d^2-7/32*c/(a*e^2+c*d^2)^2/a*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*e^3-3/32*c^2/(a*e^2+c*d^2)^2/a^2*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^2*e-7/16*c/(a*e^2+c*d^2)^2/a*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*e^3-3/16*c^2/(a*e^2+c*d^2)^2/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2*e-7/16*c/(a*e^2+c*d^2)^2/a*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*e^3-3/16*c^2/(a*e^2+c*d^2)^2/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2*e-9/32*c/(a*e^2+c*d^2)^2/a/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d*e^2-5/32*c^2/(a*e^2+c*d^2)^2/a^2/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^3-9/16*c/(a*e^2+c*d^2)^2/a/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d*e^2-5/16*c^2/(a*e^2+c*d^2)^2/a^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^3-9/16*c/(a*e^2+c*d^2)^2/a/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d*e^2-5/16*c^2/(a*e^2+c*d^2)^2/a^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^3-1/d*e^5/(a*e^2+c*d^2)^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","A"
258,1,932,577,0.021000," ","int(1/x^4/(e*x^2+d)/(c*x^4+a)^2,x)","\frac{c^{2} e^{3} x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}+\frac{c^{3} d^{2} e \,x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a^{2}}-\frac{c^{2} d \,e^{2} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a}-\frac{c^{3} d^{3} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(c \,x^{4}+a \right) a^{2}}+\frac{e^{6} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{d e}\, d^{2}}+\frac{9 \sqrt{2}\, c \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}+\frac{9 \sqrt{2}\, c \,e^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}+\frac{9 \sqrt{2}\, c \,e^{3} \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a}+\frac{5 \sqrt{2}\, c^{2} d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a^{2}}+\frac{5 \sqrt{2}\, c^{2} d^{2} e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a^{2}}+\frac{5 \sqrt{2}\, c^{2} d^{2} e \ln \left(\frac{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(\frac{a}{c}\right)^{\frac{1}{4}} a^{2}}-\frac{11 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}-\frac{11 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \,e^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}-\frac{11 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \,e^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{2}}-\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{3}}-\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{c}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{3}}-\frac{7 \left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}{x^{2}-\left(\frac{a}{c}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{c}}}\right)}{32 \left(a \,e^{2}+c \,d^{2}\right)^{2} a^{3}}+\frac{e}{a^{2} d^{2} x}-\frac{1}{3 a^{2} d \,x^{3}}"," ",0,"-1/3/a^2/d/x^3+e/a^2/d^2/x+1/4*c^2/(a*e^2+c*d^2)^2/a/(c*x^4+a)*x^3*e^3+1/4*c^3/(a*e^2+c*d^2)^2/a^2/(c*x^4+a)*x^3*e*d^2-1/4*c^2/(a*e^2+c*d^2)^2/a/(c*x^4+a)*x*d*e^2-1/4*c^3/(a*e^2+c*d^2)^2/a^2/(c*x^4+a)*x*d^3-11/16*c^2/(a*e^2+c*d^2)^2/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d*e^2-7/16*c^3/(a*e^2+c*d^2)^2/a^3*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^3-11/32*c^2/(a*e^2+c*d^2)^2/a^2*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d*e^2-7/32*c^3/(a*e^2+c*d^2)^2/a^3*(a/c)^(1/4)*2^(1/2)*ln((x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^3-11/16*c^2/(a*e^2+c*d^2)^2/a^2*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d*e^2-7/16*c^3/(a*e^2+c*d^2)^2/a^3*(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^3+9/32*c/(a*e^2+c*d^2)^2/a/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*e^3+5/32*c^2/(a*e^2+c*d^2)^2/a^2/(a/c)^(1/4)*2^(1/2)*ln((x^2-(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2))/(x^2+(a/c)^(1/4)*2^(1/2)*x+(a/c)^(1/2)))*d^2*e+9/16*c/(a*e^2+c*d^2)^2/a/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*e^3+5/16*c^2/(a*e^2+c*d^2)^2/a^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x-1)*d^2*e+9/16*c/(a*e^2+c*d^2)^2/a/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*e^3+5/16*c^2/(a*e^2+c*d^2)^2/a^2/(a/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/c)^(1/4)*x+1)*d^2*e+1/d^2*e^6/(a*e^2+c*d^2)^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","A"
259,1,110,75,0.074000," ","int(x^2/(x^2+1)/(x^4+1)^(1/2),x)","\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) x , i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}+\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}"," ",0,"1/(1/2*2^(1/2)+1/2*I*2^(1/2))*(1-I*x^2)^(1/2)*(1+I*x^2)^(1/2)/(x^4+1)^(1/2)*EllipticF(x*(1/2*2^(1/2)+1/2*I*2^(1/2)),I)+(-1)^(3/4)*(1-I*x^2)^(1/2)*(1+I*x^2)^(1/2)/(x^4+1)^(1/2)*EllipticPi((-1)^(1/4)*x,I,(-I)^(1/2)/(-1)^(1/4))","C"
260,1,112,75,0.023000," ","int(x^2/(-x^2+1)/(x^4+1)^(1/2),x)","-\frac{\sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticF \left(\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) x , i\right)}{\left(\frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right) \sqrt{x^{4}+1}}-\frac{\left(-1\right)^{\frac{3}{4}} \sqrt{-i x^{2}+1}\, \sqrt{i x^{2}+1}\, \EllipticPi \left(\left(-1\right)^{\frac{1}{4}} x , -i, -\sqrt{-i}\, \left(-1\right)^{\frac{3}{4}}\right)}{\sqrt{x^{4}+1}}"," ",0,"-1/(1/2*2^(1/2)+1/2*I*2^(1/2))*(-I*x^2+1)^(1/2)*(I*x^2+1)^(1/2)/(x^4+1)^(1/2)*EllipticF((1/2*2^(1/2)+1/2*I*2^(1/2))*x,I)-(-1)^(3/4)*(-I*x^2+1)^(1/2)*(I*x^2+1)^(1/2)/(x^4+1)^(1/2)*EllipticPi((-1)^(1/4)*x,-I,(-I)^(1/2)/(-1)^(1/4))","C"
261,1,96,81,0.019000," ","int(x^2/(x^2+1)/(-x^4+1)^(1/2),x)","-\frac{\left(-x^{2}+1\right) x}{2 \sqrt{\left(-x^{2}+1\right) \left(x^{2}+1\right)}}+\frac{\sqrt{-x^{2}+1}\, \sqrt{x^{2}+1}\, \EllipticF \left(x , i\right)}{2 \sqrt{-x^{4}+1}}+\frac{\sqrt{-x^{2}+1}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(x , i\right)+\EllipticF \left(x , i\right)\right)}{2 \sqrt{-x^{4}+1}}"," ",0,"1/2*EllipticF(x,I)*(-x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+1)^(1/2)-1/2*(-x^2+1)*x/((-x^2+1)*(x^2+1))^(1/2)+1/2*(-x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+1)^(1/2)*(EllipticF(x,I)-EllipticE(x,I))","A"
262,1,143,49,0.033000," ","int(x^2/(-x^2+1)/(-x^4+1)^(1/2),x)","-\frac{\sqrt{-x^{2}+1}\, \sqrt{x^{2}+1}\, \EllipticF \left(x , i\right)}{2 \sqrt{-x^{4}+1}}-\frac{-x^{3}+x^{2}-x +1}{4 \sqrt{\left(x +1\right) \left(-x^{3}+x^{2}-x +1\right)}}+\frac{\sqrt{-x^{2}+1}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(x , i\right)+\EllipticF \left(x , i\right)\right)}{2 \sqrt{-x^{4}+1}}-\frac{-x^{3}-x^{2}-x -1}{4 \sqrt{\left(x -1\right) \left(-x^{3}-x^{2}-x -1\right)}}"," ",0,"-1/2*EllipticF(x,I)*(-x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+1)^(1/2)-1/4*(-x^3+x^2-x+1)/((x+1)*(-x^3+x^2-x+1))^(1/2)+1/2*(-x^2+1)^(1/2)*(x^2+1)^(1/2)/(-x^4+1)^(1/2)*(EllipticF(x,I)-EllipticE(x,I))-1/4*(-x^3-x^2-x-1)/((x-1)*(-x^3-x^2-x-1))^(1/2)","B"
263,1,99,91,0.017000," ","int(x^2/(x^2+1)/(x^4-1)^(1/2),x)","\frac{\left(x^{2}-1\right) x}{2 \sqrt{\left(x^{2}+1\right) \left(x^{2}-1\right)}}-\frac{i \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticF \left(i x , i\right)}{2 \sqrt{x^{4}-1}}+\frac{i \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \left(-\EllipticE \left(i x , i\right)+\EllipticF \left(i x , i\right)\right)}{2 \sqrt{x^{4}-1}}"," ",0,"-1/2*I*(x^2+1)^(1/2)*(-x^2+1)^(1/2)/(x^4-1)^(1/2)*EllipticF(I*x,I)+1/2*(x^2-1)*x/((x^2+1)*(x^2-1))^(1/2)+1/2*I*(x^2+1)^(1/2)*(-x^2+1)^(1/2)/(x^4-1)^(1/2)*(EllipticF(I*x,I)-EllipticE(I*x,I))","A"
264,1,134,45,0.020000," ","int(x^2/(-x^2+1)/(x^4-1)^(1/2),x)","\frac{i \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \EllipticF \left(i x , i\right)}{2 \sqrt{x^{4}-1}}+\frac{x^{3}-x^{2}+x -1}{4 \sqrt{\left(x +1\right) \left(x^{3}-x^{2}+x -1\right)}}+\frac{i \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}\, \left(-\EllipticE \left(i x , i\right)+\EllipticF \left(i x , i\right)\right)}{2 \sqrt{x^{4}-1}}+\frac{x^{3}+x^{2}+x +1}{4 \sqrt{\left(x -1\right) \left(x^{3}+x^{2}+x +1\right)}}"," ",0,"1/2*I*(x^2+1)^(1/2)*(-x^2+1)^(1/2)/(x^4-1)^(1/2)*EllipticF(I*x,I)+1/4*(x^3-x^2+x-1)/((x+1)*(x^3-x^2+x-1))^(1/2)+1/2*I*(x^2+1)^(1/2)*(-x^2+1)^(1/2)/(x^4-1)^(1/2)*(EllipticF(I*x,I)-EllipticE(I*x,I))+1/4*(x^3+x^2+x+1)/((x-1)*(x^3+x^2+x+1))^(1/2)","B"
265,1,168,79,0.039000," ","int(x^2/(x^2+1)/(-x^4-1)^(1/2),x)","\frac{\sqrt{i x^{2}+1}\, \sqrt{-i x^{2}+1}\, \EllipticF \left(\left(\frac{\sqrt{2}}{2}-\frac{i \sqrt{2}}{2}\right) x , i\right)}{\left(\frac{\sqrt{2}}{2}-\frac{i \sqrt{2}}{2}\right) \sqrt{-x^{4}-1}}-\frac{i \sqrt{-i}\, \sqrt{i x^{2}+1}\, \sqrt{-i x^{2}+1}\, \EllipticPi \left(\sqrt{-i}\, x , -i, \frac{\left(-1\right)^{\frac{1}{4}}}{\sqrt{-i}}\right)}{2 \sqrt{-x^{4}-1}}-\frac{\sqrt{i x^{2}+1}\, \sqrt{-i x^{2}+1}\, \EllipticPi \left(\sqrt{-i}\, x , -i, \frac{\left(-1\right)^{\frac{1}{4}}}{\sqrt{-i}}\right)}{2 \sqrt{-i}\, \sqrt{-x^{4}-1}}"," ",0,"1/(1/2*2^(1/2)-1/2*I*2^(1/2))*(I*x^2+1)^(1/2)*(-I*x^2+1)^(1/2)/(-x^4-1)^(1/2)*EllipticF((1/2*2^(1/2)-1/2*I*2^(1/2))*x,I)-1/2*I*(-I)^(1/2)*(I*x^2+1)^(1/2)*(-I*x^2+1)^(1/2)/(-x^4-1)^(1/2)*EllipticPi((-I)^(1/2)*x,-I,(-1)^(1/4)/(-I)^(1/2))-1/2/(-I)^(1/2)*(I*x^2+1)^(1/2)*(-I*x^2+1)^(1/2)/(-x^4-1)^(1/2)*EllipticPi((-I)^(1/2)*x,-I,(-1)^(1/4)/(-I)^(1/2))","C"
266,1,115,79,0.020000," ","int(x^2/(-x^2+1)/(-x^4-1)^(1/2),x)","-\frac{\sqrt{i x^{2}+1}\, \sqrt{-i x^{2}+1}\, \EllipticF \left(\left(\frac{\sqrt{2}}{2}-\frac{i \sqrt{2}}{2}\right) x , i\right)}{\left(\frac{\sqrt{2}}{2}-\frac{i \sqrt{2}}{2}\right) \sqrt{-x^{4}-1}}+\frac{\sqrt{i x^{2}+1}\, \sqrt{-i x^{2}+1}\, \EllipticPi \left(\sqrt{-i}\, x , i, \frac{\left(-1\right)^{\frac{1}{4}}}{\sqrt{-i}}\right)}{\sqrt{-i}\, \sqrt{-x^{4}-1}}"," ",0,"-1/(1/2*2^(1/2)-1/2*I*2^(1/2))*(I*x^2+1)^(1/2)*(-I*x^2+1)^(1/2)/(-x^4-1)^(1/2)*EllipticF((1/2*2^(1/2)-1/2*I*2^(1/2))*x,I)+1/(-I)^(1/2)*(I*x^2+1)^(1/2)*(-I*x^2+1)^(1/2)/(-x^4-1)^(1/2)*EllipticPi((-I)^(1/2)*x,I,(-1)^(1/4)/(-I)^(1/2))","C"
267,1,159,179,0.011000," ","int(x^2*(d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2),x)","\frac{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(8 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b \,d^{\frac{3}{2}} x^{3}-6 a \,c^{2} d \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+3 b \,c^{3} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)-6 \sqrt{d \,x^{2}+c}\, a c \,d^{\frac{3}{2}} x +3 \sqrt{d \,x^{2}+c}\, b \,c^{2} \sqrt{d}\, x +12 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a \,d^{\frac{3}{2}} x -6 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b c \sqrt{d}\, x \right)}{48 \left(b \,x^{2}+a \right) d^{\frac{5}{2}}}"," ",0,"1/48*((b*x^2+a)^2)^(1/2)*(8*d^(3/2)*(d*x^2+c)^(3/2)*x^3*b+12*d^(3/2)*(d*x^2+c)^(3/2)*x*a-6*d^(1/2)*(d*x^2+c)^(3/2)*x*b*c-6*d^(3/2)*(d*x^2+c)^(1/2)*x*a*c+3*d^(1/2)*(d*x^2+c)^(1/2)*x*b*c^2-6*ln(d^(1/2)*x+(d*x^2+c)^(1/2))*a*c^2*d+3*ln(d^(1/2)*x+(d*x^2+c)^(1/2))*b*c^3)/(b*x^2+a)/d^(5/2)","A"
268,1,51,78,0.004000," ","int(x*(d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2),x)","\frac{\left(d \,x^{2}+c \right)^{\frac{3}{2}} \left(3 b d \,x^{2}+5 a d -2 b c \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}}{15 \left(b \,x^{2}+a \right) d^{2}}"," ",0,"1/15*(d*x^2+c)^(3/2)*(3*b*d*x^2+5*a*d-2*b*c)*((b*x^2+a)^2)^(1/2)/d^2/(b*x^2+a)","A"
269,1,119,129,0.007000," ","int((d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2),x)","\frac{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(4 a c d \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)-b \,c^{2} \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+4 \sqrt{d \,x^{2}+c}\, a \,d^{\frac{3}{2}} x -\sqrt{d \,x^{2}+c}\, b c \sqrt{d}\, x +2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} b \sqrt{d}\, x \right)}{8 \left(b \,x^{2}+a \right) d^{\frac{3}{2}}}"," ",0,"1/8*((b*x^2+a)^2)^(1/2)*(2*d^(1/2)*(d*x^2+c)^(3/2)*x*b+4*d^(3/2)*(d*x^2+c)^(1/2)*x*a-d^(1/2)*(d*x^2+c)^(1/2)*x*b*c+4*ln(d^(1/2)*x+(d*x^2+c)^(1/2))*a*c*d-ln(d^(1/2)*x+(d*x^2+c)^(1/2))*b*c^2)/(b*x^2+a)/d^(3/2)","A"
270,1,80,107,0.007000," ","int((d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x,x)","-\frac{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(3 a \sqrt{c}\, d \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)-3 \sqrt{d \,x^{2}+c}\, a d -\left(d \,x^{2}+c \right)^{\frac{3}{2}} b \right)}{3 \left(b \,x^{2}+a \right) d}"," ",0,"-1/3*((b*x^2+a)^2)^(1/2)*(3*ln(2*(c^(1/2)*(d*x^2+c)^(1/2)+c)/x)*c^(1/2)*a*d-b*(d*x^2+c)^(3/2)-3*(d*x^2+c)^(1/2)*a*d)/(b*x^2+a)/d","A"
271,1,128,130,0.013000," ","int((d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x^2,x)","\frac{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(2 a c d x \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+b \,c^{2} x \ln \left(\sqrt{d}\, x +\sqrt{d \,x^{2}+c}\right)+2 \sqrt{d \,x^{2}+c}\, a \,d^{\frac{3}{2}} x^{2}+\sqrt{d \,x^{2}+c}\, b c \sqrt{d}\, x^{2}-2 \left(d \,x^{2}+c \right)^{\frac{3}{2}} a \sqrt{d}\right)}{2 \left(b \,x^{2}+a \right) c \sqrt{d}\, x}"," ",0,"1/2*((b*x^2+a)^2)^(1/2)*(2*d^(3/2)*(d*x^2+c)^(1/2)*x^2*a+d^(1/2)*(d*x^2+c)^(1/2)*x^2*b*c-2*d^(1/2)*(d*x^2+c)^(3/2)*a+2*ln(d^(1/2)*x+(d*x^2+c)^(1/2))*x*a*c*d+ln(d^(1/2)*x+(d*x^2+c)^(1/2))*x*b*c^2)/(b*x^2+a)/c/x/d^(1/2)","A"
272,1,133,128,0.012000," ","int((d*x^2+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x^3,x)","-\frac{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(a \sqrt{c}\, d \,x^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)+2 b \,c^{\frac{3}{2}} x^{2} \ln \left(\frac{2 c +2 \sqrt{d \,x^{2}+c}\, \sqrt{c}}{x}\right)-\sqrt{d \,x^{2}+c}\, a d \,x^{2}-2 \sqrt{d \,x^{2}+c}\, b c \,x^{2}+\left(d \,x^{2}+c \right)^{\frac{3}{2}} a \right)}{2 \left(b \,x^{2}+a \right) c \,x^{2}}"," ",0,"-1/2*((b*x^2+a)^2)^(1/2)*(c^(1/2)*ln(2*(c+(d*x^2+c)^(1/2)*c^(1/2))/x)*x^2*a*d+2*c^(3/2)*ln(2*(c+(d*x^2+c)^(1/2)*c^(1/2))/x)*x^2*b-(d*x^2+c)^(1/2)*x^2*a*d-2*(d*x^2+c)^(1/2)*x^2*b*c+(d*x^2+c)^(3/2)*a)/(b*x^2+a)/c/x^2","A"
273,1,73,68,0.001000," ","int(x^3*(e*x^2+d)^2*(c*x^4+b*x^2+a),x)","\frac{c \,e^{2} x^{12}}{12}+\frac{\left(e^{2} b +2 d e c \right) x^{10}}{10}+\frac{\left(a \,e^{2}+2 d e b +c \,d^{2}\right) x^{8}}{8}+\frac{a \,d^{2} x^{4}}{4}+\frac{\left(2 d e a +d^{2} b \right) x^{6}}{6}"," ",0,"1/12*c*e^2*x^12+1/10*(b*e^2+2*c*d*e)*x^10+1/8*(a*e^2+2*b*d*e+c*d^2)*x^8+1/6*(2*a*d*e+b*d^2)*x^6+1/4*a*d^2*x^4","A"
274,1,73,68,0.001000," ","int(x^2*(e*x^2+d)^2*(c*x^4+b*x^2+a),x)","\frac{c \,e^{2} x^{11}}{11}+\frac{\left(e^{2} b +2 d e c \right) x^{9}}{9}+\frac{\left(a \,e^{2}+2 d e b +c \,d^{2}\right) x^{7}}{7}+\frac{a \,d^{2} x^{3}}{3}+\frac{\left(2 d e a +d^{2} b \right) x^{5}}{5}"," ",0,"1/11*c*e^2*x^11+1/9*(b*e^2+2*c*d*e)*x^9+1/7*(a*e^2+2*b*d*e+c*d^2)*x^7+1/5*(2*a*d*e+b*d^2)*x^5+1/3*a*d^2*x^3","A"
275,1,73,69,0.000000," ","int(x*(e*x^2+d)^2*(c*x^4+b*x^2+a),x)","\frac{c \,e^{2} x^{10}}{10}+\frac{\left(e^{2} b +2 d e c \right) x^{8}}{8}+\frac{\left(a \,e^{2}+2 d e b +c \,d^{2}\right) x^{6}}{6}+\frac{a \,d^{2} x^{2}}{2}+\frac{\left(2 d e a +d^{2} b \right) x^{4}}{4}"," ",0,"1/10*c*e^2*x^10+1/8*(b*e^2+2*c*d*e)*x^8+1/6*(a*e^2+2*b*d*e+c*d^2)*x^6+1/4*(2*a*d*e+b*d^2)*x^4+1/2*a*d^2*x^2","A"
276,1,70,65,0.002000," ","int((e*x^2+d)^2*(c*x^4+b*x^2+a),x)","\frac{c \,e^{2} x^{9}}{9}+\frac{\left(e^{2} b +2 d e c \right) x^{7}}{7}+\frac{\left(a \,e^{2}+2 d e b +c \,d^{2}\right) x^{5}}{5}+a \,d^{2} x +\frac{\left(2 d e a +d^{2} b \right) x^{3}}{3}"," ",0,"1/9*c*e^2*x^9+1/7*(b*e^2+2*c*d*e)*x^7+1/5*(a*e^2+2*b*d*e+c*d^2)*x^5+1/3*(2*a*d*e+b*d^2)*x^3+a*d^2*x","A"
277,1,77,66,0.003000," ","int((e*x^2+d)^2*(c*x^4+b*x^2+a)/x,x)","\frac{c \,e^{2} x^{8}}{8}+\frac{b \,e^{2} x^{6}}{6}+\frac{c d e \,x^{6}}{3}+\frac{a \,e^{2} x^{4}}{4}+\frac{b d e \,x^{4}}{2}+\frac{c \,d^{2} x^{4}}{4}+a d e \,x^{2}+\frac{b \,d^{2} x^{2}}{2}+a \,d^{2} \ln \left(x \right)"," ",0,"1/8*c*e^2*x^8+1/6*x^6*b*e^2+1/3*x^6*c*d*e+1/4*x^4*a*e^2+1/2*x^4*b*d*e+1/4*x^4*c*d^2+x^2*a*d*e+1/2*x^2*b*d^2+a*d^2*ln(x)","A"
278,1,75,65,0.003000," ","int((e*x^2+d)^2*(c*x^4+b*x^2+a)/x^2,x)","\frac{c \,e^{2} x^{7}}{7}+\frac{b \,e^{2} x^{5}}{5}+\frac{2 c d e \,x^{5}}{5}+\frac{a \,e^{2} x^{3}}{3}+\frac{2 b d e \,x^{3}}{3}+\frac{c \,d^{2} x^{3}}{3}+2 a d e x +b \,d^{2} x -\frac{a \,d^{2}}{x}"," ",0,"1/7*c*e^2*x^7+1/5*x^5*b*e^2+2/5*x^5*c*d*e+1/3*x^3*a*e^2+2/3*x^3*b*d*e+1/3*x^3*c*d^2+2*d*e*a*x+d^2*b*x-a*d^2/x","A"
279,1,76,66,0.007000," ","int((e*x^2+d)^2*(c*x^4+b*x^2+a)/x^3,x)","\frac{c \,e^{2} x^{6}}{6}+\frac{b \,e^{2} x^{4}}{4}+\frac{c d e \,x^{4}}{2}+\frac{a \,e^{2} x^{2}}{2}+b d e \,x^{2}+\frac{c \,d^{2} x^{2}}{2}+2 a d e \ln \left(x \right)+b \,d^{2} \ln \left(x \right)-\frac{a \,d^{2}}{2 x^{2}}"," ",0,"1/6*c*e^2*x^6+1/4*x^4*b*e^2+1/2*x^4*c*d*e+1/2*x^2*a*e^2+x^2*b*d*e+1/2*x^2*c*d^2+2*ln(x)*a*d*e+ln(x)*b*d^2-1/2*a*d^2/x^2","A"
280,1,214,150,0.013000," ","int(x^6*(c*x^4+b*x^2+a)/(e*x^2+d)^2,x)","\frac{c \,x^{7}}{7 e^{2}}+\frac{b \,x^{5}}{5 e^{2}}-\frac{2 c d \,x^{5}}{5 e^{3}}+\frac{a \,x^{3}}{3 e^{2}}-\frac{2 b d \,x^{3}}{3 e^{3}}+\frac{c \,d^{2} x^{3}}{e^{4}}-\frac{a \,d^{2} x}{2 \left(e \,x^{2}+d \right) e^{3}}+\frac{5 a \,d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{3}}+\frac{b \,d^{3} x}{2 \left(e \,x^{2}+d \right) e^{4}}-\frac{7 b \,d^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{4}}-\frac{c \,d^{4} x}{2 \left(e \,x^{2}+d \right) e^{5}}+\frac{9 c \,d^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{5}}-\frac{2 a d x}{e^{3}}+\frac{3 b \,d^{2} x}{e^{4}}-\frac{4 c \,d^{3} x}{e^{5}}"," ",0,"1/7*c*x^7/e^2+1/5/e^2*x^5*b-2/5/e^3*x^5*c*d+1/3/e^2*x^3*a-2/3/e^3*x^3*b*d+1/e^4*x^3*c*d^2-2/e^3*a*d*x+3/e^4*d^2*b*x-4/e^5*c*d^3*x-1/2*d^2/e^3*x/(e*x^2+d)*a+1/2*d^3/e^4*x/(e*x^2+d)*b-1/2*d^4/e^5*x/(e*x^2+d)*c+5/2*d^2/e^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a-7/2*d^3/e^4/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b+9/2*d^4/e^5/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
281,1,176,119,0.012000," ","int(x^4*(c*x^4+b*x^2+a)/(e*x^2+d)^2,x)","\frac{c \,x^{5}}{5 e^{2}}+\frac{b \,x^{3}}{3 e^{2}}-\frac{2 c d \,x^{3}}{3 e^{3}}+\frac{a d x}{2 \left(e \,x^{2}+d \right) e^{2}}-\frac{3 a d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{2}}-\frac{b \,d^{2} x}{2 \left(e \,x^{2}+d \right) e^{3}}+\frac{5 b \,d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{3}}+\frac{c \,d^{3} x}{2 \left(e \,x^{2}+d \right) e^{4}}-\frac{7 c \,d^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{4}}+\frac{a x}{e^{2}}-\frac{2 b d x}{e^{3}}+\frac{3 c \,d^{2} x}{e^{4}}"," ",0,"1/5*c*x^5/e^2+1/3/e^2*x^3*b-2/3/e^3*x^3*c*d+1/e^2*a*x-2/e^3*d*b*x+3/e^4*c*d^2*x+1/2*d/e^2*x/(e*x^2+d)*a-1/2*d^2/e^3*x/(e*x^2+d)*b+1/2*d^3/e^4*x/(e*x^2+d)*c-3/2*d/e^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a+5/2*d^2/e^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b-7/2*d^3/e^4/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
282,1,141,92,0.010000," ","int(x^2*(c*x^4+b*x^2+a)/(e*x^2+d)^2,x)","\frac{c \,x^{3}}{3 e^{2}}-\frac{a x}{2 \left(e \,x^{2}+d \right) e}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e}+\frac{b d x}{2 \left(e \,x^{2}+d \right) e^{2}}-\frac{3 b d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{2}}-\frac{c \,d^{2} x}{2 \left(e \,x^{2}+d \right) e^{3}}+\frac{5 c \,d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{3}}+\frac{b x}{e^{2}}-\frac{2 c d x}{e^{3}}"," ",0,"1/3*c*x^3/e^2+1/e^2*b*x-2/e^3*c*d*x-1/2/e*x/(e*x^2+d)*a+1/2/e^2*x/(e*x^2+d)*d*b-1/2/e^3*x/(e*x^2+d)*c*d^2+1/2/e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a-3/2/e^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*d*b+5/2/e^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c*d^2","A"
283,1,118,71,0.010000," ","int((c*x^4+b*x^2+a)/(e*x^2+d)^2,x)","\frac{a x}{2 \left(e \,x^{2}+d \right) d}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d}-\frac{b x}{2 \left(e \,x^{2}+d \right) e}+\frac{b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e}+\frac{c d x}{2 \left(e \,x^{2}+d \right) e^{2}}-\frac{3 c d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e^{2}}+\frac{c x}{e^{2}}"," ",0,"c*x/e^2+1/2/d*x/(e*x^2+d)*a-1/2/e*x/(e*x^2+d)*b+1/2/e^2*d*x/(e*x^2+d)*c+1/2/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a+1/2/e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b-3/2/e^2*d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
284,1,121,77,0.013000," ","int((c*x^4+b*x^2+a)/x^2/(e*x^2+d)^2,x)","-\frac{a e x}{2 \left(e \,x^{2}+d \right) d^{2}}-\frac{3 a e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d^{2}}+\frac{b x}{2 \left(e \,x^{2}+d \right) d}+\frac{b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d}-\frac{c x}{2 \left(e \,x^{2}+d \right) e}+\frac{c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, e}-\frac{a}{d^{2} x}"," ",0,"-a/d^2/x-1/2/d^2*e*x/(e*x^2+d)*a+1/2/d*x/(e*x^2+d)*b-1/2/e*x/(e*x^2+d)*c-3/2/d^2*e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a+1/2/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b+1/2/e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
285,1,146,92,0.013000," ","int((c*x^4+b*x^2+a)/x^4/(e*x^2+d)^2,x)","\frac{a \,e^{2} x}{2 \left(e \,x^{2}+d \right) d^{3}}+\frac{5 a \,e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d^{3}}-\frac{b e x}{2 \left(e \,x^{2}+d \right) d^{2}}-\frac{3 b e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d^{2}}+\frac{c x}{2 \left(e \,x^{2}+d \right) d}+\frac{c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d}+\frac{2 a e}{d^{3} x}-\frac{b}{d^{2} x}-\frac{a}{3 d^{2} x^{3}}"," ",0,"-1/3*a/d^2/x^3+2/d^3/x*a*e-1/d^2/x*b+1/2/d^3*x/(e*x^2+d)*a*e^2-1/2/d^2*x/(e*x^2+d)*e*b+1/2/d*x/(e*x^2+d)*c+5/2/d^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a*e^2-3/2/d^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*e*b+1/2/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
286,1,183,120,0.015000," ","int((c*x^4+b*x^2+a)/x^6/(e*x^2+d)^2,x)","-\frac{a \,e^{3} x}{2 \left(e \,x^{2}+d \right) d^{4}}-\frac{7 a \,e^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d^{4}}+\frac{b \,e^{2} x}{2 \left(e \,x^{2}+d \right) d^{3}}+\frac{5 b \,e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d^{3}}-\frac{c e x}{2 \left(e \,x^{2}+d \right) d^{2}}-\frac{3 c e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d^{2}}-\frac{3 a \,e^{2}}{d^{4} x}+\frac{2 b e}{d^{3} x}-\frac{c}{d^{2} x}+\frac{2 a e}{3 d^{3} x^{3}}-\frac{b}{3 d^{2} x^{3}}-\frac{a}{5 d^{2} x^{5}}"," ",0,"-1/5*a/d^2/x^5+2/3/d^3/x^3*a*e-1/3/d^2/x^3*b-3/d^4/x*a*e^2+2/d^3/x*e*b-1/d^2/x*c-1/2*e^3/d^4*x/(e*x^2+d)*a+1/2*e^2/d^3*x/(e*x^2+d)*b-1/2*e/d^2*x/(e*x^2+d)*c-7/2*e^3/d^4/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a+5/2*e^2/d^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b-3/2*e/d^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
287,1,221,150,0.016000," ","int((c*x^4+b*x^2+a)/x^8/(e*x^2+d)^2,x)","\frac{a \,e^{4} x}{2 \left(e \,x^{2}+d \right) d^{5}}+\frac{9 a \,e^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d^{5}}-\frac{b \,e^{3} x}{2 \left(e \,x^{2}+d \right) d^{4}}-\frac{7 b \,e^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d^{4}}+\frac{c \,e^{2} x}{2 \left(e \,x^{2}+d \right) d^{3}}+\frac{5 c \,e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{2 \sqrt{d e}\, d^{3}}+\frac{4 a \,e^{3}}{d^{5} x}-\frac{3 b \,e^{2}}{d^{4} x}+\frac{2 c e}{d^{3} x}-\frac{a \,e^{2}}{d^{4} x^{3}}+\frac{2 b e}{3 d^{3} x^{3}}-\frac{c}{3 d^{2} x^{3}}+\frac{2 a e}{5 d^{3} x^{5}}-\frac{b}{5 d^{2} x^{5}}-\frac{a}{7 d^{2} x^{7}}"," ",0,"-1/7*a/d^2/x^7+2/5/d^3/x^5*a*e-1/5/d^2/x^5*b-1/d^4/x^3*a*e^2+2/3/d^3/x^3*e*b-1/3/d^2/x^3*c+4*e^3/d^5/x*a-3*e^2/d^4/x*b+2*e/d^3/x*c+1/2*e^4/d^5*x/(e*x^2+d)*a-1/2*e^3/d^4*x/(e*x^2+d)*b+1/2*e^2/d^3*x/(e*x^2+d)*c+9/2*e^4/d^5/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a-7/2*e^3/d^4/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b+5/2*e^2/d^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
288,1,239,155,0.015000," ","int(x^6*(c*x^4+b*x^2+a)/(e*x^2+d)^3,x)","\frac{9 a d \,x^{3}}{8 \left(e \,x^{2}+d \right)^{2} e^{2}}-\frac{13 b \,d^{2} x^{3}}{8 \left(e \,x^{2}+d \right)^{2} e^{3}}+\frac{17 c \,d^{3} x^{3}}{8 \left(e \,x^{2}+d \right)^{2} e^{4}}+\frac{c \,x^{5}}{5 e^{3}}+\frac{7 a \,d^{2} x}{8 \left(e \,x^{2}+d \right)^{2} e^{3}}-\frac{11 b \,d^{3} x}{8 \left(e \,x^{2}+d \right)^{2} e^{4}}+\frac{b \,x^{3}}{3 e^{3}}+\frac{15 c \,d^{4} x}{8 \left(e \,x^{2}+d \right)^{2} e^{5}}-\frac{c d \,x^{3}}{e^{4}}-\frac{15 a d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{3}}+\frac{35 b \,d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{4}}-\frac{63 c \,d^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{5}}+\frac{a x}{e^{3}}-\frac{3 b d x}{e^{4}}+\frac{6 c \,d^{2} x}{e^{5}}"," ",0,"1/5*c*x^5/e^3+1/3/e^3*x^3*b-1/e^4*x^3*c*d+1/e^3*a*x-3/e^4*d*b*x+6/e^5*c*d^2*x+9/8*d/e^2/(e*x^2+d)^2*x^3*a-13/8*d^2/e^3/(e*x^2+d)^2*x^3*b+17/8*d^3/e^4/(e*x^2+d)^2*x^3*c+7/8*d^2/e^3/(e*x^2+d)^2*a*x-11/8*d^3/e^4/(e*x^2+d)^2*b*x+15/8*d^4/e^5/(e*x^2+d)^2*c*x-15/8*d/e^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a+35/8*d^2/e^4/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b-63/8*d^3/e^5/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
289,1,202,127,0.013000," ","int(x^4*(c*x^4+b*x^2+a)/(e*x^2+d)^3,x)","-\frac{5 a \,x^{3}}{8 \left(e \,x^{2}+d \right)^{2} e}+\frac{9 b d \,x^{3}}{8 \left(e \,x^{2}+d \right)^{2} e^{2}}-\frac{13 c \,d^{2} x^{3}}{8 \left(e \,x^{2}+d \right)^{2} e^{3}}-\frac{3 a d x}{8 \left(e \,x^{2}+d \right)^{2} e^{2}}+\frac{7 b \,d^{2} x}{8 \left(e \,x^{2}+d \right)^{2} e^{3}}-\frac{11 c \,d^{3} x}{8 \left(e \,x^{2}+d \right)^{2} e^{4}}+\frac{c \,x^{3}}{3 e^{3}}+\frac{3 a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{2}}-\frac{15 b d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{3}}+\frac{35 c \,d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{4}}+\frac{b x}{e^{3}}-\frac{3 c d x}{e^{4}}"," ",0,"1/3*c*x^3/e^3+1/e^3*b*x-3/e^4*c*d*x-5/8/e/(e*x^2+d)^2*x^3*a+9/8/e^2/(e*x^2+d)^2*x^3*b*d-13/8/e^3/(e*x^2+d)^2*x^3*c*d^2-3/8/e^2/(e*x^2+d)^2*a*d*x+7/8/e^3/(e*x^2+d)^2*d^2*b*x-11/8/e^4/(e*x^2+d)^2*c*d^3*x+3/8/e^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a-15/8/e^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*d*b+35/8/e^4/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c*d^2","A"
290,1,179,110,0.011000," ","int(x^2*(c*x^4+b*x^2+a)/(e*x^2+d)^3,x)","\frac{a \,x^{3}}{8 \left(e \,x^{2}+d \right)^{2} d}-\frac{5 b \,x^{3}}{8 \left(e \,x^{2}+d \right)^{2} e}+\frac{9 c d \,x^{3}}{8 \left(e \,x^{2}+d \right)^{2} e^{2}}-\frac{a x}{8 \left(e \,x^{2}+d \right)^{2} e}-\frac{3 b d x}{8 \left(e \,x^{2}+d \right)^{2} e^{2}}+\frac{7 c \,d^{2} x}{8 \left(e \,x^{2}+d \right)^{2} e^{3}}+\frac{a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d e}+\frac{3 b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{2}}-\frac{15 c d \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{3}}+\frac{c x}{e^{3}}"," ",0,"c*x/e^3+1/8/(e*x^2+d)^2/d*x^3*a-5/8/e/(e*x^2+d)^2*x^3*b+9/8/e^2/(e*x^2+d)^2*x^3*c*d-1/8/e/(e*x^2+d)^2*a*x-3/8/e^2/(e*x^2+d)^2*d*b*x+7/8/e^3/(e*x^2+d)^2*c*d^2*x+1/8/e/d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a+3/8/e^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b-15/8/e^3*d/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
291,1,131,101,0.010000," ","int((c*x^4+b*x^2+a)/(e*x^2+d)^3,x)","\frac{3 a \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{2}}+\frac{b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d e}+\frac{3 c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, e^{2}}+\frac{\frac{\left(3 a \,e^{2}+d e b -5 c \,d^{2}\right) x^{3}}{8 d^{2} e}+\frac{\left(5 a \,e^{2}-d e b -3 c \,d^{2}\right) x}{8 d \,e^{2}}}{\left(e \,x^{2}+d \right)^{2}}"," ",0,"(1/8*(3*a*e^2+b*d*e-5*c*d^2)/d^2/e*x^3+1/8*(5*a*e^2-b*d*e-3*c*d^2)/e^2/d*x)/(e*x^2+d)^2+3/8/d^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a+1/8/d/e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b+3/8/e^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
292,1,182,113,0.013000," ","int((c*x^4+b*x^2+a)/x^2/(e*x^2+d)^3,x)","-\frac{7 a \,e^{2} x^{3}}{8 \left(e \,x^{2}+d \right)^{2} d^{3}}+\frac{3 b e \,x^{3}}{8 \left(e \,x^{2}+d \right)^{2} d^{2}}+\frac{c \,x^{3}}{8 \left(e \,x^{2}+d \right)^{2} d}-\frac{9 a e x}{8 \left(e \,x^{2}+d \right)^{2} d^{2}}+\frac{5 b x}{8 \left(e \,x^{2}+d \right)^{2} d}-\frac{c x}{8 \left(e \,x^{2}+d \right)^{2} e}-\frac{15 a e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{3}}+\frac{3 b \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{2}}+\frac{c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d e}-\frac{a}{d^{3} x}"," ",0,"-a/d^3/x-7/8/d^3/(e*x^2+d)^2*x^3*a*e^2+3/8/d^2/(e*x^2+d)^2*x^3*b*e+1/8/d/(e*x^2+d)^2*x^3*c-9/8/d^2/(e*x^2+d)^2*e*a*x+5/8/d/(e*x^2+d)^2*b*x-1/8/(e*x^2+d)^2/e*x*c-15/8/d^3*e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a+3/8/d^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b+1/8/d/e/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
293,1,207,126,0.016000," ","int((c*x^4+b*x^2+a)/x^4/(e*x^2+d)^3,x)","\frac{11 a \,e^{3} x^{3}}{8 \left(e \,x^{2}+d \right)^{2} d^{4}}-\frac{7 b \,e^{2} x^{3}}{8 \left(e \,x^{2}+d \right)^{2} d^{3}}+\frac{3 c e \,x^{3}}{8 \left(e \,x^{2}+d \right)^{2} d^{2}}+\frac{13 a \,e^{2} x}{8 \left(e \,x^{2}+d \right)^{2} d^{3}}-\frac{9 b e x}{8 \left(e \,x^{2}+d \right)^{2} d^{2}}+\frac{5 c x}{8 \left(e \,x^{2}+d \right)^{2} d}+\frac{35 a \,e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{4}}-\frac{15 b e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{3}}+\frac{3 c \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{2}}+\frac{3 a e}{d^{4} x}-\frac{b}{d^{3} x}-\frac{a}{3 d^{3} x^{3}}"," ",0,"-1/3*a/d^3/x^3+3/d^4/x*a*e-1/d^3/x*b+11/8/d^4/(e*x^2+d)^2*x^3*a*e^3-7/8/d^3/(e*x^2+d)^2*x^3*b*e^2+3/8/d^2/(e*x^2+d)^2*x^3*c*e+13/8/d^3/(e*x^2+d)^2*a*e^2*x-9/8/d^2/(e*x^2+d)^2*b*e*x+5/8/d/(e*x^2+d)^2*c*x+35/8/d^4/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a*e^2-15/8/d^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*e*b+3/8/d^2/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
294,1,245,154,0.016000," ","int((c*x^4+b*x^2+a)/x^6/(e*x^2+d)^3,x)","-\frac{15 a \,e^{4} x^{3}}{8 \left(e \,x^{2}+d \right)^{2} d^{5}}+\frac{11 b \,e^{3} x^{3}}{8 \left(e \,x^{2}+d \right)^{2} d^{4}}-\frac{7 c \,e^{2} x^{3}}{8 \left(e \,x^{2}+d \right)^{2} d^{3}}-\frac{17 a \,e^{3} x}{8 \left(e \,x^{2}+d \right)^{2} d^{4}}+\frac{13 b \,e^{2} x}{8 \left(e \,x^{2}+d \right)^{2} d^{3}}-\frac{9 c e x}{8 \left(e \,x^{2}+d \right)^{2} d^{2}}-\frac{63 a \,e^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{5}}+\frac{35 b \,e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{4}}-\frac{15 c e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{8 \sqrt{d e}\, d^{3}}-\frac{6 a \,e^{2}}{d^{5} x}+\frac{3 b e}{d^{4} x}-\frac{c}{d^{3} x}+\frac{a e}{d^{4} x^{3}}-\frac{b}{3 d^{3} x^{3}}-\frac{a}{5 d^{3} x^{5}}"," ",0,"-1/5*a/d^3/x^5+1/d^4/x^3*a*e-1/3/d^3/x^3*b-6/d^5/x*a*e^2+3/d^4/x*e*b-1/d^3/x*c-15/8*e^4/d^5/(e*x^2+d)^2*x^3*a+11/8*e^3/d^4/(e*x^2+d)^2*x^3*b-7/8*e^2/d^3/(e*x^2+d)^2*x^3*c-17/8*e^3/d^4/(e*x^2+d)^2*a*x+13/8*e^2/d^3/(e*x^2+d)^2*b*x-9/8*e/d^2/(e*x^2+d)^2*c*x-63/8*e^3/d^5/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*a+35/8*e^2/d^4/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*b-15/8*e/d^3/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)*c","A"
295,1,538,216,0.016000," ","int(x^9/(e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{3 a^{2} b e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, c^{2}}+\frac{a^{2} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, c}-\frac{a \,b^{3} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, c^{3}}-\frac{2 a \,b^{2} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, c^{2}}+\frac{b^{4} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, c^{3}}-\frac{a^{2} e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) c^{2}}+\frac{a \,b^{2} e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) c^{3}}+\frac{a b d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) c^{2}}-\frac{b^{3} d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) c^{3}}+\frac{x^{4}}{4 c e}+\frac{d^{4} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) e^{3}}-\frac{b \,x^{2}}{2 c^{2} e}-\frac{d \,x^{2}}{2 c \,e^{2}}"," ",0,"1/4/c/e*x^4-1/2/c^2/e*x^2*b-1/2/c*d/e^2*x^2-1/4/(a*e^2-b*d*e+c*d^2)/c^2*ln(c*x^4+b*x^2+a)*a^2*e+1/4/(a*e^2-b*d*e+c*d^2)/c^3*ln(c*x^4+b*x^2+a)*a*b^2*e+1/2/(a*e^2-b*d*e+c*d^2)/c^2*ln(c*x^4+b*x^2+a)*a*b*d-1/4/(a*e^2-b*d*e+c*d^2)/c^3*ln(c*x^4+b*x^2+a)*b^3*d+3/2/(a*e^2-b*d*e+c*d^2)/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^2*b*e+1/(a*e^2-b*d*e+c*d^2)/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^2*d-2/(a*e^2-b*d*e+c*d^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^2*d-1/2/(a*e^2-b*d*e+c*d^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*e+1/2/(a*e^2-b*d*e+c*d^2)/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^4*d+1/2*d^4*ln(e*x^2+d)/e^3/(a*e^2-b*d*e+c*d^2)","B"
296,1,408,177,0.010000," ","int(x^7/(e*x^2+d)/(c*x^4+b*x^2+a),x)","-\frac{a^{2} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, c}+\frac{a \,b^{2} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, c^{2}}+\frac{3 a b d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, c}-\frac{b^{3} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{a b e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) c^{2}}-\frac{a d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) c}+\frac{b^{2} d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) c^{2}}-\frac{d^{3} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) e^{2}}+\frac{x^{2}}{2 c e}"," ",0,"1/2/c/e*x^2-1/4/(a*e^2-b*d*e+c*d^2)/c^2*ln(c*x^4+b*x^2+a)*a*b*e-1/4/(a*e^2-b*d*e+c*d^2)/c*ln(c*x^4+b*x^2+a)*a*d+1/4/(a*e^2-b*d*e+c*d^2)/c^2*ln(c*x^4+b*x^2+a)*b^2*d-1/(a*e^2-b*d*e+c*d^2)/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^2*e+3/2/(a*e^2-b*d*e+c*d^2)/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b*d+1/2/(a*e^2-b*d*e+c*d^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*e-1/2/(a*e^2-b*d*e+c*d^2)/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*d-1/2*d^3*ln(e*x^2+d)/e^2/(a*e^2-b*d*e+c*d^2)","B"
297,1,289,148,0.010000," ","int(x^5/(e*x^2+d)/(c*x^4+b*x^2+a),x)","-\frac{a b e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, c}-\frac{a d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{b^{2} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, c}+\frac{a e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) c}-\frac{b d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) c}+\frac{d^{2} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) e}"," ",0,"1/4/(a*e^2-b*d*e+c*d^2)/c*ln(c*x^4+b*x^2+a)*a*e-1/4/(a*e^2-b*d*e+c*d^2)/c*ln(c*x^4+b*x^2+a)*b*d-1/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*d-1/2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b/c*a*e+1/2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2/c*d+1/2*d^2*ln(e*x^2+d)/e/(a*e^2-b*d*e+c*d^2)","A"
298,1,176,122,0.008000," ","int(x^3/(e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{a e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}}-\frac{b d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}}-\frac{d \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right)}+\frac{d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a \,e^{2}-4 d e b +4 c \,d^{2}}"," ",0,"1/4*d*ln(c*x^4+b*x^2+a)/(a*e^2-b*d*e+c*d^2)+1/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*e-1/2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*d-1/2*d*ln(e*x^2+d)/(a*e^2-b*d*e+c*d^2)","A"
299,1,176,123,0.010000," ","int(x/(e*x^2+d)/(c*x^4+b*x^2+a),x)","-\frac{b e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{c d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{e \ln \left(e \,x^{2}+d \right)}{2 a \,e^{2}-2 d e b +2 c \,d^{2}}-\frac{e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right)}"," ",0,"-1/4*e*ln(c*x^4+b*x^2+a)/(a*e^2-b*d*e+c*d^2)-1/2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*e+1/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c*d+1/2*e*ln(e*x^2+d)/(a*e^2-b*d*e+c*d^2)","A"
300,1,298,157,0.011000," ","int(1/x/(e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{b^{2} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, a}-\frac{b c d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, a}-\frac{c e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{b e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) a}-\frac{c d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) a}-\frac{e^{2} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) d}+\frac{\ln \left(x \right)}{a d}"," ",0,"1/a/d*ln(x)+1/4/(a*e^2-b*d*e+c*d^2)/a*ln(c*x^4+b*x^2+a)*b*e-1/4/(a*e^2-b*d*e+c*d^2)/a*c*ln(c*x^4+b*x^2+a)*d-1/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c*e+1/2/(a*e^2-b*d*e+c*d^2)/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*e-1/2/(a*e^2-b*d*e+c*d^2)/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*c*d-1/2*e^2*ln(e*x^2+d)/d/(a*e^2-b*d*e+c*d^2)","A"
301,1,430,193,0.019000," ","int(1/x^3/(e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{3 b c e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, a}-\frac{c^{2} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, a}-\frac{b^{3} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, a^{2}}+\frac{b^{2} c d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, a^{2}}+\frac{c e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) a}-\frac{b^{2} e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) a^{2}}+\frac{b c d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) a^{2}}+\frac{e^{3} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) d^{2}}-\frac{e \ln \left(x \right)}{a \,d^{2}}-\frac{b \ln \left(x \right)}{a^{2} d}-\frac{1}{2 a d \,x^{2}}"," ",0,"-1/2/a/d/x^2-1/a/d^2*e*ln(x)-1/d/a^2*ln(x)*b+1/4/(a*e^2-b*d*e+c*d^2)/a*c*ln(c*x^4+b*x^2+a)*e-1/4/(a*e^2-b*d*e+c*d^2)/a^2*ln(c*x^4+b*x^2+a)*b^2*e+1/4/(a*e^2-b*d*e+c*d^2)/a^2*c*ln(c*x^4+b*x^2+a)*b*d+3/2/(a*e^2-b*d*e+c*d^2)/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*c*e-1/(a*e^2-b*d*e+c*d^2)/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c^2*d-1/2/(a*e^2-b*d*e+c*d^2)/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*e+1/2/(a*e^2-b*d*e+c*d^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*c*d+1/2*e^3*ln(e*x^2+d)/d^2/(a*e^2-b*d*e+c*d^2)","B"
302,1,584,254,0.020000," ","int(1/x^5/(e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{c^{2} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, a}-\frac{2 b^{2} c e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, a^{2}}+\frac{3 b \,c^{2} d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, a^{2}}+\frac{b^{4} e \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, a^{3}}-\frac{b^{3} c d \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{4 a c -b^{2}}\, a^{3}}-\frac{b c e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) a^{2}}+\frac{c^{2} d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) a^{2}}+\frac{b^{3} e \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) a^{3}}-\frac{b^{2} c d \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) a^{3}}-\frac{e^{4} \ln \left(e \,x^{2}+d \right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) d^{3}}+\frac{e^{2} \ln \left(x \right)}{a \,d^{3}}+\frac{b e \ln \left(x \right)}{a^{2} d^{2}}-\frac{c \ln \left(x \right)}{a^{2} d}+\frac{b^{2} \ln \left(x \right)}{a^{3} d}+\frac{e}{2 a \,d^{2} x^{2}}+\frac{b}{2 a^{2} d \,x^{2}}-\frac{1}{4 a d \,x^{4}}"," ",0,"-1/4/a/d/x^4+1/2/a/d^2*e/x^2+1/2/d/a^2/x^2*b+1/a/d^3*e^2*ln(x)+1/d^2/a^2*ln(x)*b*e-1/a^2*c/d*ln(x)+1/d/a^3*ln(x)*b^2-1/2/(a*e^2-b*d*e+c*d^2)/a^2*c*ln(c*x^4+b*x^2+a)*b*e+1/4/(a*e^2-b*d*e+c*d^2)/a^2*c^2*ln(c*x^4+b*x^2+a)*d+1/4/(a*e^2-b*d*e+c*d^2)/a^3*ln(c*x^4+b*x^2+a)*b^3*e-1/4/(a*e^2-b*d*e+c*d^2)/a^3*c*ln(c*x^4+b*x^2+a)*b^2*d+1/(a*e^2-b*d*e+c*d^2)/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*e*c^2-2/(a*e^2-b*d*e+c*d^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*c*e+3/2/(a*e^2-b*d*e+c*d^2)/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*d*b*c^2+1/2/(a*e^2-b*d*e+c*d^2)/a^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^4*e-1/2/(a*e^2-b*d*e+c*d^2)/a^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*c*d-1/2*e^4*ln(e*x^2+d)/d^3/(a*e^2-b*d*e+c*d^2)","B"
303,1,1449,340,0.042000," ","int(x^8/(e*x^2+d)/(c*x^4+b*x^2+a),x)","-\frac{3 \sqrt{2}\, a^{2} b e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{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^{2} b e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a \,b^{3} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, a \,b^{3} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{2 \sqrt{2}\, a \,b^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{2 \sqrt{2}\, a \,b^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{4} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, b^{4} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, a^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a \,b^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, a \,b^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, a b d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b^{3} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, b^{3} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{d^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{d e}\, e^{2}}+\frac{x^{3}}{3 c e}-\frac{b x}{c^{2} e}-\frac{d x}{c \,e^{2}}"," ",0,"1/3/c/e*x^3-1/c^2/e*b*x-1/c*d/e^2*x+1/2/(a*e^2-b*d*e+c*d^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^2*e-1/2/(a*e^2-b*d*e+c*d^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)*a*b^2*e-1/(a*e^2-b*d*e+c*d^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*b*d+1/2/(a*e^2-b*d*e+c*d^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^3*d-3/2/(a*e^2-b*d*e+c*d^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^2*b*e-1/(a*e^2-b*d*e+c*d^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*d+1/2/(a*e^2-b*d*e+c*d^2)/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^3*e+2/(a*e^2-b*d*e+c*d^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^2*d-1/2/(a*e^2-b*d*e+c*d^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^4*d-1/2/(a*e^2-b*d*e+c*d^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^2*e+1/2/(a*e^2-b*d*e+c*d^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)*a*b^2*e+1/(a*e^2-b*d*e+c*d^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*b*d-1/2/(a*e^2-b*d*e+c*d^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^3*d-3/2/(a*e^2-b*d*e+c*d^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^2*b*e-1/(a*e^2-b*d*e+c*d^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*d+1/2/(a*e^2-b*d*e+c*d^2)/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^3*e+2/(a*e^2-b*d*e+c*d^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^2*d-1/2/(a*e^2-b*d*e+c*d^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^4*d+1/e^2*d^4/(a*e^2-b*d*e+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","B"
304,1,1098,280,0.036000," ","int(x^6/(e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, a^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a \,b^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a \,b^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{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 b d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b^{3} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b^{3} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, a b e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a b e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, a d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{d^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{d e}\, e}+\frac{x}{c e}"," ",0,"1/c/e*x+1/2/(a*e^2-b*d*e+c*d^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*b*e+1/2/(a*e^2-b*d*e+c*d^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d-1/2/(a*e^2-b*d*e+c*d^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*d+1/(a*e^2-b*d*e+c*d^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*e-1/2/(a*e^2-b*d*e+c*d^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^2*e-3/2/(a*e^2-b*d*e+c*d^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*d+1/2/(a*e^2-b*d*e+c*d^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*d-1/2/(a*e^2-b*d*e+c*d^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*b*e-1/2/(a*e^2-b*d*e+c*d^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*d+1/2/(a*e^2-b*d*e+c*d^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*d+1/(a*e^2-b*d*e+c*d^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*e-1/2/(a*e^2-b*d*e+c*d^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^2*e-3/2/(a*e^2-b*d*e+c*d^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*d+1/2/(a*e^2-b*d*e+c*d^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*d-1/e*d^3/(a*e^2-b*d*e+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","B"
305,1,764,235,0.026000," ","int(x^4/(e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, a b e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a b e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{d^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{d e}}"," ",0,"-1/2/(a*e^2-b*d*e+c*d^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e+1/2/(a*e^2-b*d*e+c*d^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+1/2/(a*e^2-b*d*e+c*d^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*e+1/(a*e^2-b*d*e+c*d^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*d-1/2/(a*e^2-b*d*e+c*d^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+1/2/(a*e^2-b*d*e+c*d^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e-1/2/(a*e^2-b*d*e+c*d^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+1/2/(a*e^2-b*d*e+c*d^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b*e+1/(a*e^2-b*d*e+c*d^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*d-1/2/(a*e^2-b*d*e+c*d^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+d^2/(a*e^2-b*d*e+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","B"
306,1,478,209,0.024000," ","int(x^2/(e*x^2+d)/(c*x^4+b*x^2+a),x)","-\frac{\sqrt{2}\, a c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{d e \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{d e}}"," ",0,"-1/2/(a*e^2-b*d*e+c*d^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d-1/(a*e^2-b*d*e+c*d^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e+1/2/(a*e^2-b*d*e+c*d^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+1/2/(a*e^2-b*d*e+c*d^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d-1/(a*e^2-b*d*e+c*d^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*e+1/2/(a*e^2-b*d*e+c*d^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-d*e/(a*e^2-b*d*e+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","B"
307,1,480,208,0.027000," ","int(1/(e*x^2+d)/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, b c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{e^{2} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{d e}}"," ",0,"1/2/(a*e^2-b*d*e+c*d^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+1/2/(a*e^2-b*d*e+c*d^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-1/(a*e^2-b*d*e+c*d^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d-1/2/(a*e^2-b*d*e+c*d^2)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*e+1/2/(a*e^2-b*d*e+c*d^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e-1/(a*e^2-b*d*e+c*d^2)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+e^2/(a*e^2-b*d*e+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","B"
308,1,817,253,0.030000," ","int(1/x^2/(e*x^2+d)/(c*x^4+b*x^2+a),x)","-\frac{\sqrt{2}\, b^{2} c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b^{2} c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b \,c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, c^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{e^{3} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{d e}\, d}-\frac{1}{a d x}"," ",0,"-1/a/d/x-1/2/(a*e^2-b*d*e+c*d^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)*b*e+1/2/(a*e^2-b*d*e+c*d^2)/a*c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+1/(a*e^2-b*d*e+c*d^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)*e-1/2/(a*e^2-b*d*e+c*d^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^2*e+1/2/(a*e^2-b*d*e+c*d^2)/a*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d+1/2/(a*e^2-b*d*e+c*d^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)*b*e-1/2/(a*e^2-b*d*e+c*d^2)/a*c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+1/(a*e^2-b*d*e+c*d^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)*e-1/2/(a*e^2-b*d*e+c*d^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^2*e+1/2/(a*e^2-b*d*e+c*d^2)/a*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-1/d*e^3/(a*e^2-b*d*e+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","B"
309,1,1160,303,0.040000," ","int(1/x^4/(e*x^2+d)/(c*x^4+b*x^2+a),x)","-\frac{3 \sqrt{2}\, b \,c^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{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 \,c^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, c^{3} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, c^{3} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{3} c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b^{3} c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, b^{2} c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, b^{2} c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, c^{2} e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, c^{2} e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} c e \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, b^{2} c e \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, b \,c^{2} d \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b \,c^{2} d \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{e^{4} \arctan \left(\frac{e x}{\sqrt{d e}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{d e}\, d^{2}}+\frac{e}{a \,d^{2} x}+\frac{b}{a^{2} d x}-\frac{1}{3 a d \,x^{3}}"," ",0,"-1/3/a/d/x^3+1/a/d^2*e/x+1/d/a^2/x*b-1/2/(a*e^2-b*d*e+c*d^2)/a*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)*e+1/2/(a*e^2-b*d*e+c*d^2)/a^2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e-1/2/(a*e^2-b*d*e+c*d^2)/a^2*c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-3/2/(a*e^2-b*d*e+c*d^2)/a*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e+1/(a*e^2-b*d*e+c*d^2)/a*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+1/2/(a*e^2-b*d*e+c*d^2)/a^2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e-1/2/(a*e^2-b*d*e+c*d^2)/a^2*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+1/2/(a*e^2-b*d*e+c*d^2)/a*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)*e-1/2/(a*e^2-b*d*e+c*d^2)/a^2*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*e+1/2/(a*e^2-b*d*e+c*d^2)/a^2*c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*d-3/2/(a*e^2-b*d*e+c*d^2)/a*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b*e+1/(a*e^2-b*d*e+c*d^2)/a*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*d+1/2/(a*e^2-b*d*e+c*d^2)/a^2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3*e-1/2/(a*e^2-b*d*e+c*d^2)/a^2*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2*d+1/d^2*e^4/(a*e^2-b*d*e+c*d^2)/(d*e)^(1/2)*arctan(1/(d*e)^(1/2)*e*x)","B"
310,1,336,677,0.096000," ","int(1/(e*x^2+d)/(c*x^4+b*x^2+a)/(f*x)^(1/2),x)","\frac{f \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,f^{2} \textit{\_Z}^{4}+a \,f^{4}\right)^{4} c e -b e \,f^{2}+c d \,f^{2}\right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,f^{2} \textit{\_Z}^{4}+a \,f^{4}\right)+\sqrt{f x}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,f^{2} \textit{\_Z}^{4}+a \,f^{4}\right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,f^{2} \textit{\_Z}^{4}+a \,f^{4}\right)^{3} b \,f^{2}\right)}+\frac{\left(\frac{d \,f^{2}}{e}\right)^{\frac{1}{4}} \sqrt{2}\, e^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{f x}}{\left(\frac{d \,f^{2}}{e}\right)^{\frac{1}{4}}}-1\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) d f}+\frac{\left(\frac{d \,f^{2}}{e}\right)^{\frac{1}{4}} \sqrt{2}\, e^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{f x}}{\left(\frac{d \,f^{2}}{e}\right)^{\frac{1}{4}}}+1\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) d f}+\frac{\left(\frac{d \,f^{2}}{e}\right)^{\frac{1}{4}} \sqrt{2}\, e^{2} \ln \left(\frac{f x +\left(\frac{d \,f^{2}}{e}\right)^{\frac{1}{4}} \sqrt{f x}\, \sqrt{2}+\sqrt{\frac{d \,f^{2}}{e}}}{f x -\left(\frac{d \,f^{2}}{e}\right)^{\frac{1}{4}} \sqrt{f x}\, \sqrt{2}+\sqrt{\frac{d \,f^{2}}{e}}}\right)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) d f}"," ",0,"1/2*f/(a*e^2-b*d*e+c*d^2)*sum((-_R^4*c*e-b*e*f^2+c*d*f^2)/(2*_R^7*c+_R^3*b*f^2)*ln((f*x)^(1/2)-_R),_R=RootOf(_Z^8*c+_Z^4*b*f^2+a*f^4))+1/4/f*e^2/(a*e^2-b*d*e+c*d^2)*(d*f^2/e)^(1/4)/d*2^(1/2)*ln((f*x+(d*f^2/e)^(1/4)*(f*x)^(1/2)*2^(1/2)+(d*f^2/e)^(1/2))/(f*x-(d*f^2/e)^(1/4)*(f*x)^(1/2)*2^(1/2)+(d*f^2/e)^(1/2)))+1/2/f*e^2/(a*e^2-b*d*e+c*d^2)*(d*f^2/e)^(1/4)/d*2^(1/2)*arctan(2^(1/2)/(d*f^2/e)^(1/4)*(f*x)^(1/2)+1)+1/2/f*e^2/(a*e^2-b*d*e+c*d^2)*(d*f^2/e)^(1/4)/d*2^(1/2)*arctan(2^(1/2)/(d*f^2/e)^(1/4)*(f*x)^(1/2)-1)","C"
311,1,1049,244,0.043000," ","int(x^5*(c*x^4+b*x^2+a)^(1/2)/(e*x^2+d),x)","-\frac{a \,d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{2}}{8 c e}+\frac{b \,d^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{4}}-\frac{c \,d^{4} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, d \,x^{2}}{4 e^{2}}-\frac{a b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{8 c^{\frac{3}{2}} e}-\frac{a d \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 \sqrt{c}\, e^{2}}+\frac{b^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{5}{2}} e}+\frac{b^{2} d \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 c^{\frac{3}{2}} e^{2}}+\frac{b \,d^{2} \ln \left(\frac{\left(x^{2}+\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\right)}{4 \sqrt{c}\, e^{3}}-\frac{\sqrt{c}\, d^{3} \ln \left(\frac{\left(x^{2}+\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\right)}{2 e^{4}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2}}{16 c^{2} e}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b d}{8 c \,e^{2}}+\frac{\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, d^{2}}{2 e^{3}}+\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}{6 c e}"," ",0,"1/6*(c*x^4+b*x^2+a)^(3/2)/c/e-1/8/e*b/c*x^2*(c*x^4+b*x^2+a)^(1/2)-1/16/e*b^2/c^2*(c*x^4+b*x^2+a)^(1/2)-1/8/e*b/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))*a+1/32/e*b^3/c^(5/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/4/e^2*d*(c*x^4+b*x^2+a)^(1/2)*x^2-1/8/e^2*d/c*(c*x^4+b*x^2+a)^(1/2)*b-1/4/e^2*d/c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))*a+1/16/e^2*d/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))*b^2+1/2*d^2/e^3*(c*(x^2+d/e)^2+(b*e-2*c*d)/e*(x^2+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)+1/4*d^2/e^3*ln((1/2*(b*e-2*c*d)/e+c*(x^2+d/e))/c^(1/2)+(c*(x^2+d/e)^2+(b*e-2*c*d)/e*(x^2+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b-1/2*d^3/e^4*ln((1/2*(b*e-2*c*d)/e+c*(x^2+d/e))/c^(1/2)+(c*(x^2+d/e)^2+(b*e-2*c*d)/e*(x^2+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)-1/2*d^2/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x^2+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*(c*(x^2+d/e)^2+(b*e-2*c*d)/e*(x^2+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a+1/2*d^3/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x^2+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*(c*(x^2+d/e)^2+(b*e-2*c*d)/e*(x^2+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b-1/2*d^4/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x^2+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*(c*(x^2+d/e)^2+(b*e-2*c*d)/e*(x^2+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*c","B"
312,1,887,184,0.010000," ","int(x^3*(c*x^4+b*x^2+a)^(1/2)/(e*x^2+d),x)","\frac{a d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{b \,d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{c \,d^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{4}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{2}}{4 e}+\frac{a \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 \sqrt{c}\, e}-\frac{b^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 c^{\frac{3}{2}} e}-\frac{b d \ln \left(\frac{\left(x^{2}+\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\right)}{4 \sqrt{c}\, e^{2}}+\frac{\sqrt{c}\, d^{2} \ln \left(\frac{\left(x^{2}+\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\right)}{2 e^{3}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{8 c e}-\frac{\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, d}{2 e^{2}}"," ",0,"1/4/e*(c*x^4+b*x^2+a)^(1/2)*x^2+1/8/e/c*(c*x^4+b*x^2+a)^(1/2)*b+1/4/e/c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))*a-1/16/e/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))*b^2-1/2*d/e^2*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)-1/4*d/e^2*ln(((x^2+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b+1/2*d^2/e^3*ln(((x^2+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)+1/2*d/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a-1/2*d^2/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b+1/2*d^3/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*c","B"
313,1,757,144,0.005000," ","int(x*(c*x^4+b*x^2+a)^(1/2)/(e*x^2+d),x)","-\frac{a \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e}+\frac{b d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{c \,d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{b \ln \left(\frac{\left(x^{2}+\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\right)}{4 \sqrt{c}\, e}-\frac{\sqrt{c}\, d \ln \left(\frac{\left(x^{2}+\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\right)}{2 e^{2}}+\frac{\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{2 e}"," ",0,"1/2/e*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)+1/4/e*ln(((x^2+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b-1/2/e^2*ln(((x^2+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d-1/2/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a+1/2/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*d*b-1/2/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*c*d^2","B"
314,1,851,156,0.017000," ","int((c*x^4+b*x^2+a)^(1/2)/x/(e*x^2+d),x)","\frac{a \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, d}-\frac{b \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e}+\frac{c d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{\sqrt{a}\, \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2 d}+\frac{b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 \sqrt{c}\, d}-\frac{b \ln \left(\frac{\left(x^{2}+\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\right)}{4 \sqrt{c}\, d}+\frac{\sqrt{c}\, \ln \left(\frac{\left(x^{2}+\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\right)}{2 e}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{2 d}-\frac{\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{2 d}"," ",0,"1/2/d*(c*x^4+b*x^2+a)^(1/2)+1/4/d*b*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)-1/2/d*a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-1/2/d*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)-1/4/d*ln(((x^2+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b+1/2/e*ln(((x^2+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)+1/2/d/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a-1/2/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b+1/2/e^2*d/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*c","B"
315,1,1009,297,0.020000," ","int((c*x^4+b*x^2+a)^(1/2)/x^3/(e*x^2+d),x)","-\frac{a e \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, d^{2}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{2}}{2 a d}+\frac{b \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, d}-\frac{c \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e}+\frac{\sqrt{a}\, e \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2 d^{2}}-\frac{b \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{4 \sqrt{a}\, d}-\frac{b e \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 \sqrt{c}\, d^{2}}+\frac{b e \ln \left(\frac{\left(x^{2}+\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\right)}{4 \sqrt{c}\, d^{2}}+\frac{\sqrt{c}\, \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2 d}-\frac{\sqrt{c}\, \ln \left(\frac{\left(x^{2}+\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\right)}{2 d}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{2 a d}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, e}{2 d^{2}}+\frac{\sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e}{2 d^{2}}-\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}{2 a d \,x^{2}}"," ",0,"-1/2/d^2*e*(c*x^4+b*x^2+a)^(1/2)-1/4/d^2*e*b*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)+1/2/d^2*e*a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+1/2*e/d^2*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)+1/4*e/d^2*ln(((x^2+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b-1/2/d*ln(((x^2+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)-1/2*e/d^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a+1/2/d/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b-1/2/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*c-1/2/d/a/x^2*(c*x^4+b*x^2+a)^(3/2)+1/2/d*b/a*(c*x^4+b*x^2+a)^(1/2)-1/4/d*b/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+1/2/d/a*c*(c*x^4+b*x^2+a)^(1/2)*x^2+1/2/d*c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))","B"
316,1,528,416,0.101000," ","int(x^4*(2*x^4+2*x^2+1)^(1/2)/(2*x^2+3),x)","\frac{\sqrt{2 x^{4}+2 x^{2}+1}\, x^{3}}{10}-\frac{13 \sqrt{2 x^{4}+2 x^{2}+1}\, x}{60}+\frac{9 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{8 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{9 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{8 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{8 \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{15 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{9 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{4 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{9 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{8 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{15 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{8 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\left(\frac{13}{60}-\frac{13 i}{60}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"1/10*x^3*(2*x^4+2*x^2+1)^(1/2)-13/60*x*(2*x^4+2*x^2+1)^(1/2)-8/15/(-1+I)^(1/2)*(1+(1-I)*x^2)^(1/2)*(1+(1+I)*x^2)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF(x*(-1+I)^(1/2),1/2*2^(1/2)+1/2*I*2^(1/2))+(13/60-13/60*I)/(-1+I)^(1/2)*(1+(1-I)*x^2)^(1/2)*(1+(1+I)*x^2)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF(x*(-1+I)^(1/2),1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE(x*(-1+I)^(1/2),1/2*2^(1/2)+1/2*I*2^(1/2)))-9/4/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF(x*(-1+I)^(1/2),1/2*2^(1/2)+1/2*I*2^(1/2))+9/8*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF(x*(-1+I)^(1/2),1/2*2^(1/2)+1/2*I*2^(1/2))+9/8/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE(x*(-1+I)^(1/2),1/2*2^(1/2)+1/2*I*2^(1/2))-9/8*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE(x*(-1+I)^(1/2),1/2*2^(1/2)+1/2*I*2^(1/2))+15/8/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi(x*(-1+I)^(1/2),1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
317,1,509,409,0.009000," ","int(x^2*(2*x^4+2*x^2+1)^(1/2)/(2*x^2+3),x)","\frac{\sqrt{2 x^{4}+2 x^{2}+1}\, x}{6}-\frac{3 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{4 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{3 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{4 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{3 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{3 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{2 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{3 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{4 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{5 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{4 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\left(-\frac{1}{6}+\frac{i}{6}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"1/6*(2*x^4+2*x^2+1)^(1/2)*x+1/3/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+(-1/6+1/6*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))+3/2/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-3/4*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-3/4/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+3/4*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-5/4/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
318,1,341,384,0.006000," ","int((2*x^4+2*x^2+1)^(1/2)/(2*x^2+3),x)","\frac{\sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{2 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{2 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{\sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{2 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{5 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{6 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-1/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+1/2*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+1/2/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-1/2*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+5/6/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
319,1,511,393,0.013000," ","int((2*x^4+2*x^2+1)^(1/2)/x^2/(2*x^2+3),x)","-\frac{\sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{3 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{3 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{2 \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{3 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{2 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{3 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{3 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{5 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{9 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{\sqrt{2 x^{4}+2 x^{2}+1}}{3 x}+\frac{\left(-\frac{2}{3}+\frac{2 i}{3}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-1/3*(2*x^4+2*x^2+1)^(1/2)/x+2/3/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+(-2/3+2/3*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))+2/3/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-1/3*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-1/3/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+1/3*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-5/9/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
320,1,448,362,0.021000," ","int((2*x^4+2*x^2+1)^(1/2)/x^4/(2*x^2+3),x)","\frac{2 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{9 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{2 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{9 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{4 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{9 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{2 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{9 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{10 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{27 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{\sqrt{2 x^{4}+2 x^{2}+1}}{9 x^{3}}+\frac{\left(\frac{2}{9}-\frac{2 i}{9}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"(2/9-2/9*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))-4/9/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+2/9*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+2/9/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-2/9*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+10/27/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))-1/9*(2*x^4+2*x^2+1)^(1/2)/x^3","C"
321,1,549,539,0.020000," ","int((2*x^4+2*x^2+1)^(1/2)/x^6/(2*x^2+3),x)","\frac{4 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{27 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{4 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{27 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{4 \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{45 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{8 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{27 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{4 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{27 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{20 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{81 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{4 \sqrt{2 x^{4}+2 x^{2}+1}}{45 x}+\frac{4 \sqrt{2 x^{4}+2 x^{2}+1}}{135 x^{3}}-\frac{\sqrt{2 x^{4}+2 x^{2}+1}}{15 x^{5}}+\frac{\left(-\frac{32}{135}+\frac{32 i}{135}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-4/45*(2*x^4+2*x^2+1)^(1/2)/x-4/45/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+4/27*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+8/27/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-4/27*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-4/27/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+(-32/135+32/135*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))-20/81/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))+4/135*(2*x^4+2*x^2+1)^(1/2)/x^3-1/15*(2*x^4+2*x^2+1)^(1/2)/x^5","C"
322,1,2068,450,0.062000," ","int(x^5*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d),x)","\frac{11 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{6}}{80 e}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,d^{3}}{8 e^{4}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,d^{4}}{2 e^{5}}+\frac{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,d^{2}}{3 e^{3}}-\frac{c^{\frac{3}{2}} d^{5} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2 e^{6}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2}}{10 c e}-\frac{3 b^{5} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{512 c^{\frac{7}{2}} e}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,x^{4}}{5 e}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{4}}{256 c^{3} e}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{8}}{10 e}-\frac{b^{2} d^{4} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{3 a^{2} b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{3}{2}} e}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} x^{4}}{160 c e}-\frac{c^{2} d^{6} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{7}}-\frac{a^{2} d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{b c \,d^{5} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{6}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3} x^{2}}{128 c^{2} e}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,b^{2}}{64 c^{2} e}+\frac{3 a \,b^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{64 c^{\frac{5}{2}} e}-\frac{3 a^{2} d \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 \sqrt{c}\, e^{2}}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a d \,x^{2}}{16 e^{2}}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3} d}{128 c^{2} e^{2}}-\frac{3 b^{4} d \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{256 c^{\frac{5}{2}} e^{2}}-\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b d \,x^{4}}{16 e^{2}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c d \,x^{6}}{8 e^{2}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,d^{2} x^{4}}{6 e^{3}}+\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,d^{2} x^{2}}{24 e^{3}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} d^{2}}{16 c \,e^{3}}-\frac{b^{3} d^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{3}{2}} e^{3}}-\frac{3 a \sqrt{c}\, d^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 e^{4}}-\frac{3 b^{2} d^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 \sqrt{c}\, e^{4}}+\frac{3 b \sqrt{c}\, d^{4} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 e^{5}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,d^{3} x^{2}}{4 e^{4}}+\frac{a b \,d^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{4}}-\frac{a c \,d^{4} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{5}}+\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a b \,x^{2}}{160 c e}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} d \,x^{2}}{64 c \,e^{2}}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a b d}{32 c \,e^{2}}+\frac{3 a \,b^{2} d \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{3}{2}} e^{2}}+\frac{3 a b \,d^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{8 \sqrt{c}\, e^{3}}"," ",0,"11/80/e*b*x^6*(c*x^4+b*x^2+a)^(1/2)-5/8*d^3/e^4*b*(c*x^4+b*x^2+a)^(1/2)+1/2*d^4/e^5*c*(c*x^4+b*x^2+a)^(1/2)+2/3*d^2/e^3*a*(c*x^4+b*x^2+a)^(1/2)-1/2*d^5/e^6*c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+1/10/e*a^2/c*(c*x^4+b*x^2+a)^(1/2)-3/512/e*b^5/c^(7/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+1/5/e*a*x^4*(c*x^4+b*x^2+a)^(1/2)+3/256/e*b^4/c^3*(c*x^4+b*x^2+a)^(1/2)+1/10/e*c*x^8*(c*x^4+b*x^2+a)^(1/2)-3/32/e*a^2*b/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+1/160/e*b^2*x^4/c*(c*x^4+b*x^2+a)^(1/2)-1/128/e*b^3/c^2*x^2*(c*x^4+b*x^2+a)^(1/2)-5/64/e*a*b^2/c^2*(c*x^4+b*x^2+a)^(1/2)+3/64/e*a*b^3/c^(5/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-3/16/e^2*d*a^2*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)-5/16/e^2*d*a*x^2*(c*x^4+b*x^2+a)^(1/2)+3/128/e^2*d*b^3/c^2*(c*x^4+b*x^2+a)^(1/2)-3/256/e^2*d*b^4/c^(5/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-3/16/e^2*d*b*x^4*(c*x^4+b*x^2+a)^(1/2)-1/8/e^2*d*c*x^6*(c*x^4+b*x^2+a)^(1/2)+1/6*d^2/e^3*c*x^4*(c*x^4+b*x^2+a)^(1/2)+7/24*d^2/e^3*b*x^2*(c*x^4+b*x^2+a)^(1/2)+1/16*d^2/e^3/c*b^2*(c*x^4+b*x^2+a)^(1/2)-1/32*d^2/e^3*b^3/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-3/4*d^3/e^4*a*c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-3/16*d^3/e^4*b^2*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)+3/4*d^4/e^5*b*c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/4*d^3/e^4*x^2*c*(c*x^4+b*x^2+a)^(1/2)-1/2*d^2/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a^2-1/2*d^4/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b^2-1/2*d^6/e^7/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*c^2+7/160/e*a*b*x^2/c*(c*x^4+b*x^2+a)^(1/2)-1/64/e^2*d*b^2*x^2/c*(c*x^4+b*x^2+a)^(1/2)-5/32/e^2*d*a*b/c*(c*x^4+b*x^2+a)^(1/2)+3/32/e^2*d*a*b^2/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+3/8*d^2/e^3*a*b*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)+d^3/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a*b-d^4/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a*c+d^5/e^6/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b*c","B"
323,1,1696,332,0.014000," ","int(x^3*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} x^{2}}{64 c e}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a b}{32 c e}+\frac{c^{\frac{3}{2}} d^{4} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2 e^{5}}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,d^{2}}{8 e^{3}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,d^{3}}{2 e^{4}}-\frac{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a d}{3 e^{2}}+\frac{3 a^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 \sqrt{c}\, e}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,x^{2}}{16 e}-\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3}}{128 c^{2} e}+\frac{3 b^{4} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{256 c^{\frac{5}{2}} e}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{4}}{16 e}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{6}}{8 e}+\frac{b^{2} d^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{4}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c d \,x^{4}}{6 e^{2}}-\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b d \,x^{2}}{24 e^{2}}+\frac{c^{2} d^{5} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{6}}-\frac{3 b \sqrt{c}\, d^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 e^{4}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,d^{2} x^{2}}{4 e^{3}}+\frac{a^{2} d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{b c \,d^{4} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} d}{16 c \,e^{2}}+\frac{b^{3} d \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{3}{2}} e^{2}}+\frac{3 a \sqrt{c}\, d^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 e^{3}}+\frac{3 b^{2} d^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 \sqrt{c}\, e^{3}}-\frac{3 a \,b^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{3}{2}} e}-\frac{3 a b d \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{8 \sqrt{c}\, e^{2}}-\frac{a b \,d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{a c \,d^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{4}}"," ",0,"1/64/e*b^2*x^2/c*(c*x^4+b*x^2+a)^(1/2)+5/32/e*a*b/c*(c*x^4+b*x^2+a)^(1/2)+1/2*d^4/e^5*c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+5/8*d^2/e^3*b*(c*x^4+b*x^2+a)^(1/2)-1/2*d^3/e^4*c*(c*x^4+b*x^2+a)^(1/2)-2/3*d/e^2*a*(c*x^4+b*x^2+a)^(1/2)+3/16/e*a^2*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)+5/16/e*a*x^2*(c*x^4+b*x^2+a)^(1/2)-3/128/e*b^3/c^2*(c*x^4+b*x^2+a)^(1/2)+3/256/e*b^4/c^(5/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+3/16/e*b*x^4*(c*x^4+b*x^2+a)^(1/2)+1/8/e*c*x^6*(c*x^4+b*x^2+a)^(1/2)+1/2*d^5/e^6/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*c^2-1/6*d/e^2*c*x^4*(c*x^4+b*x^2+a)^(1/2)-7/24*d/e^2*b*x^2*(c*x^4+b*x^2+a)^(1/2)-3/4*d^3/e^4*b*c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+1/4*d^2/e^3*x^2*c*(c*x^4+b*x^2+a)^(1/2)+1/2*d/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a^2+1/2*d^3/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b^2-1/16*d/e^2/c*b^2*(c*x^4+b*x^2+a)^(1/2)+1/32*d/e^2*b^3/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+3/4*d^2/e^3*a*c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+3/16*d^2/e^3*b^2*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)-3/32/e*a*b^2/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-3/8*d/e^2*a*b*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)-d^2/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a*b+d^3/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a*c-d^4/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b*c","B"
324,1,1411,241,0.007000," ","int(x*(c*x^4+b*x^2+a)^(3/2)/(e*x^2+d),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{4}}{6 e}-\frac{a^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e}+\frac{a b d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{a c \,d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{b^{2} d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{b c \,d^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{4}}+\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{2}}{24 e}-\frac{c^{2} d^{4} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c d \,x^{2}}{4 e^{2}}+\frac{3 a b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{8 \sqrt{c}\, e}-\frac{3 a \sqrt{c}\, d \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 e^{2}}-\frac{b^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{3}{2}} e}-\frac{3 b^{2} d \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 \sqrt{c}\, e^{2}}+\frac{3 b \sqrt{c}\, d^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 e^{3}}-\frac{c^{\frac{3}{2}} d^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2 e^{4}}+\frac{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{3 e}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2}}{16 c e}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b d}{8 e^{2}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,d^{2}}{2 e^{3}}"," ",0,"1/6/e*c*x^4*(c*x^4+b*x^2+a)^(1/2)+7/24/e*b*x^2*(c*x^4+b*x^2+a)^(1/2)+1/16/e/c*b^2*(c*x^4+b*x^2+a)^(1/2)-5/8/e^2*b*(c*x^4+b*x^2+a)^(1/2)*d+1/2/e^3*c*(c*x^4+b*x^2+a)^(1/2)*d^2-1/32/e*b^3/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-3/4/e^2*a*d*c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-3/16/e^2*b^2*d*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)+3/4/e^3*b*c^(1/2)*d^2*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+2/3/e*a*(c*x^4+b*x^2+a)^(1/2)-1/4/e^2*x^2*c*(c*x^4+b*x^2+a)^(1/2)*d+3/8/e*a*b*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)-1/2/e^4*c^(3/2)*d^3*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/2/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a^2+1/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a*b*d-1/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a*c*d^2-1/2/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b^2*d^2+1/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b*c*d^3-1/2/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*c^2*d^4","B"
325,1,1270,302,0.036000," ","int((c*x^4+b*x^2+a)^(3/2)/x/(e*x^2+d),x)","\frac{a^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, d}-\frac{a b \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e}+\frac{a c d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{2}}+\frac{b^{2} d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{b c \,d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{c^{2} d^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{4}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{2}}{4 e}-\frac{a^{\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 d}+\frac{3 a \sqrt{c}\, \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 e}+\frac{3 b^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 \sqrt{c}\, e}-\frac{3 b \sqrt{c}\, d \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 e^{2}}+\frac{c^{\frac{3}{2}} d^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2 e^{3}}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{8 e}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c d}{2 e^{2}}"," ",0,"5/8/e*b*(c*x^4+b*x^2+a)^(1/2)-1/2/d*a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-1/2/e^2*d*c*(c*x^4+b*x^2+a)^(1/2)+3/4/e*a*c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+3/16/e*b^2*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)+1/4/e*x^2*c*(c*x^4+b*x^2+a)^(1/2)+1/2/e^3*d^2*c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+1/2/d/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a^2+1/e^2*d/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a*c-1/e^3*d^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b*c-3/4/e^2*d*b*c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a*b+1/2/e^2*d/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b^2+1/2/e^4*d^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*c^2","B"
326,1,1207,486,0.033000," ","int((c*x^4+b*x^2+a)^(3/2)/x^3/(e*x^2+d),x)","-\frac{a^{2} e \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, d^{2}}+\frac{a b \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, d}-\frac{a c \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e}-\frac{b^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e}+\frac{b c d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{c^{2} d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{a^{\frac{3}{2}} e \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2 d^{2}}-\frac{3 \sqrt{a}\, b \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{4 d}+\frac{3 b \sqrt{c}\, \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 e}-\frac{c^{\frac{3}{2}} d \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2 e^{2}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c}{2 e}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{2 d \,x^{2}}"," ",0,"1/2/e*c*(c*x^4+b*x^2+a)^(1/2)-3/4/d*a^(1/2)*b*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-1/2/d*a/x^2*(c*x^4+b*x^2+a)^(1/2)+3/4/e*b*c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/2/e^2*d*c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/2/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b^2+1/2/d^2*e*a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-1/2*e/d^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a^2+1/d/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a*b-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*a*c-1/2/e^3*d^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*c^2+1/e^2*d/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))*b*c","B"
327,1,547,447,0.036000," ","int(x^2*(2*x^4+2*x^2+1)^(3/2)/(-2*x^2+3),x)","-\frac{\sqrt{2 x^{4}+2 x^{2}+1}\, x^{5}}{7}-\frac{37 \sqrt{2 x^{4}+2 x^{2}+1}\, x^{3}}{70}-\frac{223 \sqrt{2 x^{4}+2 x^{2}+1}\, x}{140}-\frac{309 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{40 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{309 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{40 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{9 \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{35 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{531 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{20 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{309 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{40 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{289 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , -\frac{1}{3}-\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{8 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\left(\frac{6}{35}-\frac{6 i}{35}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-1/7*x^5*(2*x^4+2*x^2+1)^(1/2)-37/70*(2*x^4+2*x^2+1)^(1/2)*x^3-223/140*(2*x^4+2*x^2+1)^(1/2)*x-9/35/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+(6/35-6/35*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))-531/20/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-309/40*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-309/40/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+309/40*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+289/8/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,-1/3-1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
328,1,377,418,0.007000," ","int((2*x^4+2*x^2+1)^(3/2)/(-2*x^2+3),x)","-\frac{\sqrt{2 x^{4}+2 x^{2}+1}\, x^{3}}{5}-\frac{9 \sqrt{2 x^{4}+2 x^{2}+1}\, x}{10}-\frac{103 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{20 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{103 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{20 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{177 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{10 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{103 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{20 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{289 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , -\frac{1}{3}-\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{12 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-1/5*(2*x^4+2*x^2+1)^(1/2)*x^3-9/10*(2*x^4+2*x^2+1)^(1/2)*x-177/10/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-103/20*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-103/20/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+103/20*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+289/12/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,-1/3-1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
329,1,528,603,0.016000," ","int((2*x^4+2*x^2+1)^(3/2)/x^2/(-2*x^2+3),x)","-\frac{\sqrt{2 x^{4}+2 x^{2}+1}\, x}{3}-\frac{103 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{30 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{103 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{30 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{59 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{5 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{103 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{30 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{16 \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{15 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{289 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , -\frac{1}{3}-\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{18 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{\sqrt{2 x^{4}+2 x^{2}+1}}{3 x}+\frac{\left(-\frac{14}{15}+\frac{14 i}{15}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-1/3*(2*x^4+2*x^2+1)^(1/2)*x-59/5/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-103/30*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-103/30/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+103/30*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+289/18/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,-1/3-1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))-1/3*(2*x^4+2*x^2+1)^(1/2)/x+16/15/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+(-14/15+14/15*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))","C"
330,1,530,631,0.017000," ","int((2*x^4+2*x^2+1)^(3/2)/x^4/(-2*x^2+3),x)","\frac{103 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{45 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{103 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{45 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{118 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{15 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{103 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{45 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{44 \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{15 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{289 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , -\frac{1}{3}-\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{27 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{10 \sqrt{2 x^{4}+2 x^{2}+1}}{9 x}-\frac{\sqrt{2 x^{4}+2 x^{2}+1}}{9 x^{3}}+\frac{\left(-\frac{12}{5}+\frac{12 i}{5}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-118/15/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+103/45*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-103/45/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-103/45*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+289/27/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,-1/3-1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))-10/9*(2*x^4+2*x^2+1)^(1/2)/x+44/15/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+(-12/5+12/5*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))-1/9*(2*x^4+2*x^2+1)^(1/2)/x^3","C"
331,1,549,546,0.018000," ","int((2*x^4+2*x^2+1)^(3/2)/x^6/(-2*x^2+3),x)","\frac{206 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{135 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{206 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{135 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{236 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{45 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{206 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{135 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{184 \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{45 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{578 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , -\frac{1}{3}-\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{81 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{262 \sqrt{2 x^{4}+2 x^{2}+1}}{135 x}-\frac{46 \sqrt{2 x^{4}+2 x^{2}+1}}{135 x^{3}}-\frac{\sqrt{2 x^{4}+2 x^{2}+1}}{15 x^{5}}+\frac{\left(-\frac{52}{15}+\frac{52 i}{15}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-236/45/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+206/135*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-206/135/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-206/135*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+578/81/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,-1/3-1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))-262/135*(2*x^4+2*x^2+1)^(1/2)/x+184/45/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+(-52/15+52/15*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))-46/135*(2*x^4+2*x^2+1)^(1/2)/x^3-1/15*(2*x^4+2*x^2+1)^(1/2)/x^5","C"
332,1,267,149,0.020000," ","int(x^5/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 c^{\frac{3}{2}} e}-\frac{d \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2 \sqrt{c}\, e^{2}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{2 c e}"," ",0,"1/2*(c*x^4+b*x^2+a)^(1/2)/c/e-1/4/e*b/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/2/e^2*d*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)-1/2*d^2/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))","A"
333,1,204,117,0.010000," ","int(x^3/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","\frac{d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{2}}+\frac{\ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2 \sqrt{c}\, e}"," ",0,"1/2/e*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)+1/2*d/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))","A"
334,1,165,76,0.007000," ","int(x/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{\ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e}"," ",0,"-1/2/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))","B"
335,1,207,118,0.010000," ","int(1/x/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, d}-\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}\, d}"," ",0,"-1/2/d/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+1/2/d/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))","A"
336,1,276,184,0.011000," ","int(1/x^3/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{e \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, d^{2}}+\frac{e \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}\, d^{2}}+\frac{b \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}} d}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{2 a d \,x^{2}}"," ",0,"1/2/d^2*e/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-1/2*e/d^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))-1/2*(c*x^4+b*x^2+a)^(1/2)/a/d/x^2+1/4/d*b/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
337,1,222,408,0.022000," ","int(x^4/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x)","-\frac{3 \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{4 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{3 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{4 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\left(-\frac{1}{4}+\frac{i}{4}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"(-1/4+1/4*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))-3/4/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+3/4/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
338,1,134,244,0.009000," ","int(x^2/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x)","\frac{\sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{2 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{\sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{2 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"1/2/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-1/2/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
339,1,70,244,0.006000," ","int(1/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x)","\frac{\sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{3 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"1/3/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
340,1,178,395,0.016000," ","int(1/x^2/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x)","-\frac{2 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{9 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{\sqrt{2 x^{4}+2 x^{2}+1}}{3 x}+\frac{\left(-\frac{1}{3}+\frac{i}{3}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-1/3*(2*x^4+2*x^2+1)^(1/2)/x+(-1/3+1/3*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))-2/9/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
341,1,260,414,0.014000," ","int(1/x^4/(2*x^2+3)/(2*x^4+2*x^2+1)^(1/2),x)","-\frac{2 \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{9 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{4 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{27 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{2 \sqrt{2 x^{4}+2 x^{2}+1}}{3 x}-\frac{\sqrt{2 x^{4}+2 x^{2}+1}}{9 x^{3}}+\frac{\left(\frac{2}{3}-\frac{2 i}{3}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"2/3*(2*x^4+2*x^2+1)^(1/2)/x+(2/3-2/3*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))+4/27/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))-1/9*(2*x^4+2*x^2+1)^(1/2)/x^3-2/9/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))","C"
342,1,720,214,0.063000," ","int(x^7/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","-\frac{2 c \,d^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e^{2}}+\frac{b^{2} x^{2}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, c e}-\frac{2 \sqrt{\left(x^{2}+\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} c -\sqrt{-4 a c +b^{2}}\, \left(x^{2}+\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}\, c \,d^{3}}{\left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(-4 a c +b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) e^{3}}+\frac{2 \sqrt{\left(x^{2}-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} c +\sqrt{-4 a c +b^{2}}\, \left(x^{2}-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}\, c \,d^{3}}{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(-4 a c +b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) e^{3}}+\frac{b^{3}}{4 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2} e}-\frac{x^{2}}{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c e}+\frac{\left(2 c \,x^{2}+b \right) d^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, e^{3}}+\frac{\left(b \,x^{2}+2 a \right) d}{\sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(4 a c -b^{2}\right) e^{2}}+\frac{\ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2 c^{\frac{3}{2}} e}+\frac{b}{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2} e}"," ",0,"-1/2/e*x^2/c/(c*x^4+b*x^2+a)^(1/2)+1/4/e*b/c^2/(c*x^4+b*x^2+a)^(1/2)+1/2/e*b^2/c/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*x^2+1/4/e*b^3/c^2/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)+1/2/e/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+d/e^2/(c*x^4+b*x^2+a)^(1/2)*(b*x^2+2*a)/(4*a*c-b^2)+d^2/e^3*(2*c*x^2+b)/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)-2*d^3/e^3*c/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(-4*a*c+b^2)/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*(c*(x^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2-(-4*a*c+b^2)^(1/2)*(x^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)-2*d^3/e^2*c/(e*(-4*a*c+b^2)^(1/2)-b*e+2*c*d)/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))+2*d^3/e^3*c/(e*(-4*a*c+b^2)^(1/2)-b*e+2*c*d)/(-4*a*c+b^2)/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*(c*(x^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2+(-4*a*c+b^2)^(1/2)*(x^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))^(1/2)","B"
343,1,613,156,0.015000," ","int(x^5/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","\frac{2 c \,d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, e}-\frac{b \,x^{2}}{\sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(4 a c -b^{2}\right) e}-\frac{2 c d \,x^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, e^{2}}+\frac{2 \sqrt{\left(x^{2}+\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} c -\sqrt{-4 a c +b^{2}}\, \left(x^{2}+\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}\, c \,d^{2}}{\left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(-4 a c +b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) e^{2}}-\frac{2 \sqrt{\left(x^{2}-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} c +\sqrt{-4 a c +b^{2}}\, \left(x^{2}-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}\, c \,d^{2}}{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(-4 a c +b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) e^{2}}-\frac{2 a}{\sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(4 a c -b^{2}\right) e}-\frac{b d}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, e^{2}}"," ",0,"-1/e/(c*x^4+b*x^2+a)^(1/2)/(4*a*c-b^2)*x^2*b-2/e/(c*x^4+b*x^2+a)^(1/2)/(4*a*c-b^2)*a-2/e^2*d/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*c*x^2-1/e^2*d/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*b+2*d^2/e^2*c/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)/(-4*a*c+b^2)/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*((x^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*c-(-4*a*c+b^2)^(1/2)*(x^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)+2*d^2/e*c/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))-2*d^2/e^2*c/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)/(-4*a*c+b^2)/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*((x^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*c+(-4*a*c+b^2)^(1/2)*(x^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))^(1/2)","B"
344,1,506,147,0.011000," ","int(x^3/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","-\frac{2 c d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}-\frac{2 \sqrt{\left(x^{2}+\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} c -\sqrt{-4 a c +b^{2}}\, \left(x^{2}+\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}\, c d}{\left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(-4 a c +b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) e}+\frac{2 \sqrt{\left(x^{2}-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} c +\sqrt{-4 a c +b^{2}}\, \left(x^{2}-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}\, c d}{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(-4 a c +b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) e}+\frac{2 c \,x^{2}+b}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, e}"," ",0,"1/e*(2*c*x^2+b)/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)-2*d/e*c/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)/(-4*a*c+b^2)/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*((x^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*c-(-4*a*c+b^2)^(1/2)*(x^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)-2*d*c/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))+2*d/e*c/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)/(-4*a*c+b^2)/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*((x^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*c+(-4*a*c+b^2)^(1/2)*(x^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))^(1/2)","B"
345,1,454,154,0.008000," ","int(x/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","\frac{2 c e \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}+\frac{2 \sqrt{\left(x^{2}+\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} c -\sqrt{-4 a c +b^{2}}\, \left(x^{2}+\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}\, c}{\left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(-4 a c +b^{2}\right) \left(x^{2}+\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{2 \sqrt{\left(x^{2}-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} c +\sqrt{-4 a c +b^{2}}\, \left(x^{2}-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}\, c}{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(-4 a c +b^{2}\right) \left(x^{2}-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}"," ",0,"2*c/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)/(-4*a*c+b^2)/(x^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)*((x^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*c-(-4*a*c+b^2)^(1/2)*(x^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)+2*c*e/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))-2*c/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)/(-4*a*c+b^2)/(x^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)*((x^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*c+(-4*a*c+b^2)^(1/2)*(x^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))^(1/2)","B"
346,1,612,242,0.024000," ","int(1/x/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","-\frac{2 c \,e^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, d}-\frac{b c \,x^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a d}-\frac{2 \sqrt{\left(x^{2}+\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} c -\sqrt{-4 a c +b^{2}}\, \left(x^{2}+\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}\, c e}{\left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(-4 a c +b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) d}+\frac{2 \sqrt{\left(x^{2}-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} c +\sqrt{-4 a c +b^{2}}\, \left(x^{2}-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}\, c e}{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(-4 a c +b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) d}-\frac{b^{2}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a d}-\frac{\ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2 a^{\frac{3}{2}} d}+\frac{1}{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a d}"," ",0,"1/2/d/a/(c*x^4+b*x^2+a)^(1/2)-1/d*b/a/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*c*x^2-1/2/d*b^2/a/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)-1/2/d/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-2*e/d*c/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)/(-4*a*c+b^2)/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*((x^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*c-(-4*a*c+b^2)^(1/2)*(x^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)-2*e^2/d*c/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))+2*e/d*c/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)/(-4*a*c+b^2)/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*((x^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*c+(-4*a*c+b^2)^(1/2)*(x^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))^(1/2)","B"
347,1,863,379,0.028000," ","int(1/x^3/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","\frac{2 c \,e^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 d e b +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x^{2}+\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x^{2}+\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}}{x^{2}+\frac{d}{e}}\right)}{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \sqrt{\frac{a \,e^{2}-d e b +c \,d^{2}}{e^{2}}}\, d^{2}}+\frac{b c e \,x^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,d^{2}}-\frac{4 c^{2} x^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a d}+\frac{3 b^{2} c \,x^{2}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2} d}+\frac{2 \sqrt{\left(x^{2}+\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} c -\sqrt{-4 a c +b^{2}}\, \left(x^{2}+\frac{b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}\, c \,e^{2}}{\left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(-4 a c +b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) d^{2}}-\frac{2 \sqrt{\left(x^{2}-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)^{2} c +\sqrt{-4 a c +b^{2}}\, \left(x^{2}-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 c}\right)}\, c \,e^{2}}{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(-4 a c +b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) d^{2}}+\frac{b^{2} e}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,d^{2}}-\frac{2 b c}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a d}+\frac{3 b^{3}}{4 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2} d}+\frac{e \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2 a^{\frac{3}{2}} d^{2}}+\frac{3 b \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{5}{2}} d}-\frac{e}{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,d^{2}}-\frac{3 b}{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2} d}-\frac{1}{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a d \,x^{2}}"," ",0,"-1/2/d^2*e/a/(c*x^4+b*x^2+a)^(1/2)+1/d^2*e*b/a/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*c*x^2+1/2/d^2*e*b^2/a/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)+1/2/d^2*e/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+2*e^2/d^2*c/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)/(-4*a*c+b^2)/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*((x^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c)^2*c-(-4*a*c+b^2)^(1/2)*(x^2+1/2*(b+(-4*a*c+b^2)^(1/2))/c))^(1/2)+2*e^3/d^2*c/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x^2+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x^2+d/e)^2*c+(b*e-2*c*d)*(x^2+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x^2+d/e))-2*e^2/d^2*c/(-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)/(-4*a*c+b^2)/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*((x^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c)^2*c+(-4*a*c+b^2)^(1/2)*(x^2-1/2*(-b+(-4*a*c+b^2)^(1/2))/c))^(1/2)-1/2/d/a/x^2/(c*x^4+b*x^2+a)^(1/2)-3/4/d*b/a^2/(c*x^4+b*x^2+a)^(1/2)+3/2/d*b^2/a^2/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*c*x^2+3/4/d*b^3/a^2/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)+3/4/d*b/a^(5/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-4/d*c^2/a/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*x^2-2/d*c/a/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*b","B"
348,1,603,435,0.046000," ","int(x^8/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x)","\frac{27 x^{3}}{16 \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{x}{8 \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{243 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{160 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{243 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{160 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{11 \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{4 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{243 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{160 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{81 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{160 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{27 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{40 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\frac{3}{8} x^{3}+\frac{3}{8} x}{\sqrt{2 x^{4}+2 x^{2}+1}}-\frac{9 \left(-\frac{1}{4} x^{3}-\frac{1}{8} x \right)}{2 \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\left(\frac{47}{32}-\frac{47 i}{32}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{81 \left(\frac{3}{20} x^{3}+\frac{1}{20} x \right)}{4 \sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"1/8*x/(2*x^4+2*x^2+1)^(1/2)-11/4/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-243/160*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+3*(1/8*x^3+1/8*x)/(2*x^4+2*x^2+1)^(1/2)+243/160*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-9/2*(-1/4*x^3-1/8*x)/(2*x^4+2*x^2+1)^(1/2)+(47/32-47/32*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))+27/16*x^3/(2*x^4+2*x^2+1)^(1/2)-81/4*(3/20*x^3+1/20*x)/(2*x^4+2*x^2+1)^(1/2)+81/160/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+243/160/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+27/40/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
349,1,586,413,0.010000," ","int(x^6/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x)","-\frac{9 x^{3}}{8 \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{81 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{80 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{81 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{80 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{7 \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{4 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{27 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{80 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{81 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{80 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{9 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{20 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{2 \left(\frac{1}{8} x^{3}+\frac{1}{8} x \right)}{\sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\left(-\frac{17}{16}+\frac{17 i}{16}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{-\frac{3}{4} x^{3}-\frac{3}{8} x}{\sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\frac{81}{40} x^{3}+\frac{27}{40} x}{\sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-2*(1/8*x^3+1/8*x)/(2*x^4+2*x^2+1)^(1/2)+7/4/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+(-17/16+17/16*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))+3*(-1/4*x^3-1/8*x)/(2*x^4+2*x^2+1)^(1/2)-9/8/(2*x^4+2*x^2+1)^(1/2)*x^3+27/2*(3/20*x^3+1/20*x)/(2*x^4+2*x^2+1)^(1/2)-27/80/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-81/80*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-81/80/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+81/80*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-9/20/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
350,1,561,412,0.010000," ","int(x^4/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x)","\frac{3 x^{3}}{4 \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{27 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{40 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{27 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{40 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{\sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{9 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{40 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{27 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{40 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{3 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{10 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{2 \left(-\frac{1}{4} x^{3}-\frac{1}{8} x \right)}{\sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\left(\frac{5}{8}-\frac{5 i}{8}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{9 \left(\frac{3}{20} x^{3}+\frac{1}{20} x \right)}{\sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-2*(-1/4*x^3-1/8*x)/(2*x^4+2*x^2+1)^(1/2)-1/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+(5/8-5/8*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))+3/4/(2*x^4+2*x^2+1)^(1/2)*x^3-9*(3/20*x^3+1/20*x)/(2*x^4+2*x^2+1)^(1/2)+9/40/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+27/40*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+27/40/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-27/40*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+3/10/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
351,1,536,413,0.010000," ","int(x^2/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x)","-\frac{x^{3}}{2 \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{9 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{20 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{9 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{20 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{2 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{3 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{20 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{9 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{20 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{\sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{5 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\left(-\frac{1}{4}+\frac{i}{4}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\frac{9}{10} x^{3}+\frac{3}{10} x}{\sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-1/2/(2*x^4+2*x^2+1)^(1/2)*x^3+1/2/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+(-1/4+1/4*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))+6*(3/20*x^3+1/20*x)/(2*x^4+2*x^2+1)^(1/2)-3/20/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-9/20*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-9/20/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+9/20*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-1/5/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
352,1,366,414,0.007000," ","int(1/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x)","\frac{3 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{10 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{3 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{10 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{10 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{3 i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{10 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{2 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{15 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{4 \left(\frac{3}{20} x^{3}+\frac{1}{20} x \right)}{\sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-4*(3/20*x^3+1/20*x)/(2*x^4+2*x^2+1)^(1/2)+1/10/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+3/10*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+3/10/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-3/10*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+2/15/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
353,1,553,452,0.018000," ","int(1/x^2/(2*x^2+3)/(2*x^4+2*x^2+1)^(3/2),x)","-\frac{x}{3 \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{\sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{5 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{5 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{\sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{3 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{\sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{15 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{i \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)}{5 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{4 \sqrt{-i x^{2}+x^{2}+1}\, \sqrt{i x^{2}+x^{2}+1}\, \EllipticPi \left(\sqrt{-1+i}\, x , \frac{1}{3}+\frac{i}{3}, \frac{\sqrt{-1-i}}{\sqrt{-1+i}}\right)}{45 \sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}-\frac{\sqrt{2 x^{4}+2 x^{2}+1}}{3 x}+\frac{\left(-\frac{1}{3}+\frac{i}{3}\right) \sqrt{\left(1-i\right) x^{2}+1}\, \sqrt{\left(1+i\right) x^{2}+1}\, \left(-\EllipticE \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)+\EllipticF \left(\sqrt{-1+i}\, x , \frac{\sqrt{2}}{2}+\frac{i \sqrt{2}}{2}\right)\right)}{\sqrt{-1+i}\, \sqrt{2 x^{4}+2 x^{2}+1}}+\frac{\frac{2}{5} x^{3}+\frac{2}{15} x}{\sqrt{2 x^{4}+2 x^{2}+1}}"," ",0,"-1/3*(2*x^4+2*x^2+1)^(1/2)/x-1/3/(2*x^4+2*x^2+1)^(1/2)*x-1/3/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+(-1/3+1/3*I)/(-1+I)^(1/2)*((1-I)*x^2+1)^(1/2)*((1+I)*x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*(EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2)))+8/3*(3/20*x^3+1/20*x)/(2*x^4+2*x^2+1)^(1/2)-1/15/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-1/5*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticF((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-1/5/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))+1/5*I/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticE((-1+I)^(1/2)*x,1/2*2^(1/2)+1/2*I*2^(1/2))-4/45/(-1+I)^(1/2)*(-I*x^2+x^2+1)^(1/2)*(I*x^2+x^2+1)^(1/2)/(2*x^4+2*x^2+1)^(1/2)*EllipticPi((-1+I)^(1/2)*x,1/3+1/3*I,(-1-I)^(1/2)/(-1+I)^(1/2))","C"
354,1,496,355,0.059000," ","int(x^7*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x)","\frac{a \sqrt{e}\, x}{2 c^{2}}-\frac{b^{2} \sqrt{e}\, x}{2 c^{3}}-\frac{a d}{2 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) c^{2}}+\frac{b^{2} d}{2 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) c^{3}}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} x^{2}}{5 c e}-\frac{\sqrt{e \,x^{2}+d}\, a}{2 c^{2}}+\frac{\sqrt{e \,x^{2}+d}\, b^{2}}{2 c^{3}}-\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} b}{3 c^{2} e}-\frac{2 \left(e \,x^{2}+d \right)^{\frac{3}{2}} d}{15 c \,e^{2}}-\frac{\left(2 a b c \,d^{3} e -a \,c^{2} d^{4}-b^{3} d^{3} e +b^{2} c \,d^{4}+\left(-2 a b c e +a \,c^{2} d +b^{3} e -b^{2} c d \right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{6}+\left(-4 a^{2} c \,e^{2}+4 a \,b^{2} e^{2}+2 a b c d e -3 a \,c^{2} d^{2}-3 b^{3} d e +3 b^{2} c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{4}+\left(4 a^{2} c \,e^{2}-4 a \,b^{2} e^{2}-2 a b c d e +3 a \,c^{2} d^{2}+3 b^{3} d e -3 b^{2} c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{2} d \right) \ln \left(-\sqrt{e}\, x -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)+\sqrt{e \,x^{2}+d}\right)}{4 c^{3} \left(\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{7} c +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} b e -3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} c d +8 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} b d e +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} c \,d^{2}+\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) b \,d^{2} e -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) c \,d^{3}\right)}"," ",0,"1/5/c*x^2*(e*x^2+d)^(3/2)/e-2/15/c*d/e^2*(e*x^2+d)^(3/2)-1/3/c^2*b*(e*x^2+d)^(3/2)/e+1/2/c^2*e^(1/2)*x*a-1/2/c^3*e^(1/2)*x*b^2-1/2/c^2*(e*x^2+d)^(1/2)*a+1/2/c^3*(e*x^2+d)^(1/2)*b^2-1/4/c^3*sum(((-2*a*b*c*e+a*c^2*d+b^3*e-b^2*c*d)*_R^6+(-4*a^2*c*e^2+4*a*b^2*e^2+2*a*b*c*d*e-3*a*c^2*d^2-3*b^3*d*e+3*b^2*c*d^2)*_R^4+d*(4*a^2*c*e^2-4*a*b^2*e^2-2*a*b*c*d*e+3*a*c^2*d^2+3*b^3*d*e-3*b^2*c*d^2)*_R^2+2*a*b*c*d^3*e-a*c^2*d^4-b^3*d^3*e+b^2*c*d^4)/(_R^7*c+3*_R^5*b*e-3*_R^5*c*d+8*_R^3*a*e^2-4*_R^3*b*d*e+3*_R^3*c*d^2+_R*b*d^2*e-_R*c*d^3)*ln((e*x^2+d)^(1/2)-e^(1/2)*x-_R),_R=RootOf(c*_Z^8+(4*b*e-4*c*d)*_Z^6+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^4+(4*b*d^2*e-4*c*d^3)*_Z^2+c*d^4))-1/2/c^2*d/((e*x^2+d)^(1/2)-e^(1/2)*x)*a+1/2/c^3*d/((e*x^2+d)^(1/2)-e^(1/2)*x)*b^2","C"
355,1,332,279,0.033000," ","int(x^5*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x)","\frac{b \sqrt{e}\, x}{2 c^{2}}-\frac{b d}{2 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) c^{2}}-\frac{\sqrt{e \,x^{2}+d}\, b}{2 c^{2}}-\frac{\left(\left(a c e -b^{2} e +b c d \right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{6}-a c \,d^{3} e +b^{2} d^{3} e -b c \,d^{4}+\left(-4 a b \,e^{2}+a c d e +3 b^{2} d e -3 b c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{4}+\left(4 a b \,e^{2}-a c d e -3 b^{2} d e +3 b c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{2} d \right) \ln \left(-\sqrt{e}\, x -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)+\sqrt{e \,x^{2}+d}\right)}{4 c^{2} \left(\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{7} c +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} b e -3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} c d +8 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} b d e +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} c \,d^{2}+\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) b \,d^{2} e -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) c \,d^{3}\right)}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}{3 c e}"," ",0,"1/3*(e*x^2+d)^(3/2)/c/e+1/2/c^2*b*e^(1/2)*x-1/2*b*(e*x^2+d)^(1/2)/c^2-1/4/c^2*sum(((a*c*e-b^2*e+b*c*d)*_R^6+(-4*a*b*e^2+a*c*d*e+3*b^2*d*e-3*b*c*d^2)*_R^4+d*(4*a*b*e^2-a*c*d*e-3*b^2*d*e+3*b*c*d^2)*_R^2-a*c*d^3*e+b^2*d^3*e-c*d^4*b)/(_R^7*c+3*_R^5*b*e-3*_R^5*c*d+8*_R^3*a*e^2-4*_R^3*b*d*e+3*_R^3*c*d^2+_R*b*d^2*e-_R*c*d^3)*ln(-e^(1/2)*x-_R+(e*x^2+d)^(1/2)),_R=RootOf(_Z^8*c+(4*b*e-4*c*d)*_Z^6+c*d^4+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^4+(4*b*d^2*e-4*c*d^3)*_Z^2))-1/2/c^2*b*d/(-e^(1/2)*x+(e*x^2+d)^(1/2))","C"
356,1,275,247,0.026000," ","int(x^3*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x)","-\frac{\sqrt{e}\, x}{2 c}+\frac{d}{2 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) c}+\frac{\left(\left(-b e +c d \right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{6}+b \,d^{3} e -c \,d^{4}+\left(-4 a \,e^{2}+3 d e b -3 c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{4}+\left(4 a \,e^{2}-3 d e b +3 c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{2} d \right) \ln \left(-\sqrt{e}\, x -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)+\sqrt{e \,x^{2}+d}\right)}{4 c \left(\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{7} c +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} b e -3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} c d +8 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} b d e +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} c \,d^{2}+\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) b \,d^{2} e -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) c \,d^{3}\right)}+\frac{\sqrt{e \,x^{2}+d}}{2 c}"," ",0,"-1/2/c*e^(1/2)*x+1/2*(e*x^2+d)^(1/2)/c+1/4/c*sum(((-b*e+c*d)*_R^6+(-4*a*e^2+3*b*d*e-3*c*d^2)*_R^4+d*(4*a*e^2-3*b*d*e+3*c*d^2)*_R^2+b*d^3*e-c*d^4)/(_R^7*c+3*_R^5*b*e-3*_R^5*c*d+8*_R^3*a*e^2-4*_R^3*b*d*e+3*_R^3*c*d^2+_R*b*d^2*e-_R*c*d^3)*ln(-e^(1/2)*x-_R+(e*x^2+d)^(1/2)),_R=RootOf(_Z^8*c+(4*b*e-4*c*d)*_Z^6+c*d^4+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^4+(4*b*d^2*e-4*c*d^3)*_Z^2))+1/2/c*d/(-e^(1/2)*x+(e*x^2+d)^(1/2))","C"
357,1,177,163,0.016000," ","int(x*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x)","\frac{e \left(\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{6}+\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{4} d -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{2} d^{2}-d^{3}\right) \ln \left(-\sqrt{e}\, x -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)+\sqrt{e \,x^{2}+d}\right)}{4 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{7} c +12 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} b e -12 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} c d +32 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} a \,e^{2}-16 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} b d e +12 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} c \,d^{2}+4 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) b \,d^{2} e -4 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) c \,d^{3}}"," ",0,"1/4*e*sum((_R^6+_R^4*d-_R^2*d^2-d^3)/(_R^7*c+3*_R^5*b*e-3*_R^5*c*d+8*_R^3*a*e^2-4*_R^3*b*d*e+3*_R^3*c*d^2+_R*b*d^2*e-_R*c*d^3)*ln(-e^(1/2)*x-_R+(e*x^2+d)^(1/2)),_R=RootOf(_Z^8*c+(4*b*e-4*c*d)*_Z^6+c*d^4+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^4+(4*b*d^2*e-4*c*d^3)*_Z^2))","C"
358,1,294,232,0.030000," ","int((e*x^2+d)^(1/2)/x/(c*x^4+b*x^2+a),x)","-\frac{\sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{e \,x^{2}+d}\, \sqrt{d}}{x}\right)}{a}+\frac{\sqrt{e}\, x}{2 a}-\frac{d}{2 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) a}-\frac{\left(\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{6} c d -c \,d^{4}+\left(-4 a \,e^{2}+4 d e b -3 c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{4}+\left(4 a \,e^{2}-4 d e b +3 c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{2} d \right) \ln \left(-\sqrt{e}\, x -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)+\sqrt{e \,x^{2}+d}\right)}{4 a \left(\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{7} c +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} b e -3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} c d +8 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} b d e +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} c \,d^{2}+\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) b \,d^{2} e -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) c \,d^{3}\right)}+\frac{\sqrt{e \,x^{2}+d}}{2 a}"," ",0,"-1/a*d^(1/2)*ln((2*d+2*d^(1/2)*(e*x^2+d)^(1/2))/x)+1/2/a*(e*x^2+d)^(1/2)+1/2/a*e^(1/2)*x-1/4/a*sum((_R^6*c*d+(-4*a*e^2+4*b*d*e-3*c*d^2)*_R^4+d*(4*a*e^2-4*b*d*e+3*c*d^2)*_R^2-c*d^4)/(_R^7*c+3*_R^5*b*e-3*_R^5*c*d+8*_R^3*a*e^2-4*_R^3*b*d*e+3*_R^3*c*d^2+_R*b*d^2*e-_R*c*d^3)*ln(-e^(1/2)*x-_R+(e*x^2+d)^(1/2)),_R=RootOf(_Z^8*c+(4*b*e-4*c*d)*_Z^6+c*d^4+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^4+(4*b*d^2*e-4*c*d^3)*_Z^2))-1/2/a*d/(-e^(1/2)*x+(e*x^2+d)^(1/2))","C"
359,1,401,309,0.030000," ","int((e*x^2+d)^(1/2)/x^3/(c*x^4+b*x^2+a),x)","-\frac{e \ln \left(\frac{2 d +2 \sqrt{e \,x^{2}+d}\, \sqrt{d}}{x}\right)}{2 a \sqrt{d}}+\frac{b \sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{e \,x^{2}+d}\, \sqrt{d}}{x}\right)}{a^{2}}-\frac{b \sqrt{e}\, x}{2 a^{2}}+\frac{b d}{2 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) a^{2}}+\frac{\sqrt{e \,x^{2}+d}\, e}{2 a d}-\frac{\sqrt{e \,x^{2}+d}\, b}{2 a^{2}}+\frac{\left(\left(-a e +b d \right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{6} c +a c \,d^{3} e -b c \,d^{4}+\left(-4 a b \,e^{2}-a c d e +4 b^{2} d e -3 b c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{4}+\left(4 a b \,e^{2}+a c d e -4 b^{2} d e +3 b c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{2} d \right) \ln \left(-\sqrt{e}\, x -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)+\sqrt{e \,x^{2}+d}\right)}{4 a^{2} \left(\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{7} c +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} b e -3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} c d +8 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} b d e +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} c \,d^{2}+\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) b \,d^{2} e -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) c \,d^{3}\right)}-\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}{2 a d \,x^{2}}"," ",0,"1/a^2*b*d^(1/2)*ln((2*d+2*(e*x^2+d)^(1/2)*d^(1/2))/x)-1/2/a^2*b*(e*x^2+d)^(1/2)-1/2/a^2*e^(1/2)*x*b+1/4/a^2*sum((c*(-a*e+b*d)*_R^6+(-4*a*b*e^2-a*c*d*e+4*b^2*d*e-3*b*c*d^2)*_R^4+d*(4*a*b*e^2+a*c*d*e-4*b^2*d*e+3*b*c*d^2)*_R^2+a*c*d^3*e-b*c*d^4)/(_R^7*c+3*_R^5*b*e-3*_R^5*c*d+8*_R^3*a*e^2-4*_R^3*b*d*e+3*_R^3*c*d^2+_R*b*d^2*e-_R*c*d^3)*ln(-e^(1/2)*x-_R+(e*x^2+d)^(1/2)),_R=RootOf(_Z^8*c+(4*b*e-4*c*d)*_Z^6+c*d^4+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^4+(4*b*d^2*e-4*c*d^3)*_Z^2))+1/2/a^2*b*d/(-e^(1/2)*x+(e*x^2+d)^(1/2))-1/2/a/d/x^2*(e*x^2+d)^(3/2)-1/2/a*e/d^(1/2)*ln((2*d+2*(e*x^2+d)^(1/2)*d^(1/2))/x)+1/2/a*e/d*(e*x^2+d)^(1/2)","C"
360,1,655,467,0.035000," ","int((e*x^2+d)^(1/2)/x^5/(c*x^4+b*x^2+a),x)","\frac{e^{2} \ln \left(\frac{2 d +2 \sqrt{e \,x^{2}+d}\, \sqrt{d}}{x}\right)}{8 a \,d^{\frac{3}{2}}}+\frac{b e \ln \left(\frac{2 d +2 \sqrt{e \,x^{2}+d}\, \sqrt{d}}{x}\right)}{2 a^{2} \sqrt{d}}+\frac{c \sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{e \,x^{2}+d}\, \sqrt{d}}{x}\right)}{a^{2}}-\frac{c \sqrt{e}\, x}{2 a^{2}}-\frac{b^{2} \sqrt{d}\, \ln \left(\frac{2 d +2 \sqrt{e \,x^{2}+d}\, \sqrt{d}}{x}\right)}{a^{3}}+\frac{b^{2} \sqrt{e}\, x}{2 a^{3}}+\frac{c d}{2 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) a^{2}}-\frac{b^{2} d}{2 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) a^{3}}-\frac{\sqrt{e \,x^{2}+d}\, e^{2}}{8 a \,d^{2}}-\frac{\sqrt{e \,x^{2}+d}\, b e}{2 a^{2} d}-\frac{\sqrt{e \,x^{2}+d}\, c}{2 a^{2}}+\frac{\sqrt{e \,x^{2}+d}\, b^{2}}{2 a^{3}}+\frac{\left(\left(a b e +a c d -b^{2} d \right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{6} c -a b c \,d^{3} e -a \,c^{2} d^{4}+b^{2} c \,d^{4}+\left(-4 a^{2} c \,e^{2}+4 a \,b^{2} e^{2}+5 a b c d e -3 a \,c^{2} d^{2}-4 b^{3} d e +3 b^{2} c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{4}+\left(4 a^{2} c \,e^{2}-4 a \,b^{2} e^{2}-5 a b c d e +3 a \,c^{2} d^{2}+4 b^{3} d e -3 b^{2} c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{2} d \right) \ln \left(-\sqrt{e}\, x -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)+\sqrt{e \,x^{2}+d}\right)}{4 a^{3} \left(\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{7} c +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} b e -3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} c d +8 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} b d e +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} c \,d^{2}+\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) b \,d^{2} e -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) c \,d^{3}\right)}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} e}{8 a \,d^{2} x^{2}}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} b}{2 a^{2} d \,x^{2}}-\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}{4 a d \,x^{4}}"," ",0,"1/a^2*d^(1/2)*ln((2*d+2*(e*x^2+d)^(1/2)*d^(1/2))/x)*c-1/a^3*d^(1/2)*ln((2*d+2*(e*x^2+d)^(1/2)*d^(1/2))/x)*b^2-1/2/a^2*(e*x^2+d)^(1/2)*c+1/2/a^3*(e*x^2+d)^(1/2)*b^2-1/2/a^2*e^(1/2)*x*c+1/2/a^3*e^(1/2)*x*b^2+1/4/a^3*sum((c*(a*b*e+a*c*d-b^2*d)*_R^6+(-4*a^2*c*e^2+4*a*b^2*e^2+5*a*b*c*d*e-3*a*c^2*d^2-4*b^3*d*e+3*b^2*c*d^2)*_R^4+d*(4*a^2*c*e^2-4*a*b^2*e^2-5*a*b*c*d*e+3*a*c^2*d^2+4*b^3*d*e-3*b^2*c*d^2)*_R^2-a*b*c*d^3*e-a*c^2*d^4+b^2*c*d^4)/(_R^7*c+3*_R^5*b*e-3*_R^5*c*d+8*_R^3*a*e^2-4*_R^3*b*d*e+3*_R^3*c*d^2+_R*b*d^2*e-_R*c*d^3)*ln(-e^(1/2)*x-_R+(e*x^2+d)^(1/2)),_R=RootOf(_Z^8*c+(4*b*e-4*c*d)*_Z^6+c*d^4+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^4+(4*b*d^2*e-4*c*d^3)*_Z^2))+1/2/a^2*d/(-e^(1/2)*x+(e*x^2+d)^(1/2))*c-1/2/a^3*d/(-e^(1/2)*x+(e*x^2+d)^(1/2))*b^2-1/4/a/d/x^4*(e*x^2+d)^(3/2)+1/8/a*e/d^2/x^2*(e*x^2+d)^(3/2)+1/8/a*e^2/d^(3/2)*ln((2*d+2*(e*x^2+d)^(1/2)*d^(1/2))/x)-1/8/a*e^2/d^2*(e*x^2+d)^(1/2)+1/2/a^2*b/d/x^2*(e*x^2+d)^(3/2)+1/2/a^2*b*e/d^(1/2)*ln((2*d+2*(e*x^2+d)^(1/2)*d^(1/2))/x)-1/2/a^2*b*e/d*(e*x^2+d)^(1/2)","C"
361,1,290,337,0.040000," ","int(x^4*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x)","\frac{b \sqrt{e}\, \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{c^{2}}+\frac{d \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{2 c \sqrt{e}}+\frac{\sqrt{e \,x^{2}+d}\, x}{2 c}+\frac{\sqrt{e}\, \left(a c \,d^{2} e -b^{2} d^{2} e +b c \,d^{3}+\left(a c e -b^{2} e +b c d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2}+2 \left(-2 a b \,e^{2}+a c d e +b^{2} d e -b c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 c^{2} \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}"," ",0,"1/2*x*(e*x^2+d)^(1/2)/c+1/2/c*d/e^(1/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))+1/2/c^2*e^(1/2)*sum(((a*c*e-b^2*e+b*c*d)*_R^2+2*(-2*a*b*e^2+a*c*d*e+b^2*d*e-b*c*d^2)*_R+e*c*d^2*a-b^2*d^2*e+b*c*d^3)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln((-e^(1/2)*x+(e*x^2+d)^(1/2))^2-_R),_R=RootOf(c*_Z^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z+c*d^4))+1/c^2*e^(1/2)*b*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))","C"
362,1,224,277,0.027000," ","int(x^2*(e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x)","-\frac{\sqrt{e}\, \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{c}+\frac{\sqrt{e}\, \left(b \,d^{2} e -c \,d^{3}+\left(b e -c d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2}+2 \left(2 a \,e^{2}-d e b +c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 c \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}"," ",0,"1/2*e^(1/2)/c*sum(((b*e-c*d)*_R^2+2*(2*a*e^2-b*d*e+c*d^2)*_R+b*d^2*e-c*d^3)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))-e^(1/2)/c*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))","C"
363,1,161,200,0.018000," ","int((e*x^2+d)^(1/2)/(c*x^4+b*x^2+a),x)","-\frac{e^{\frac{3}{2}} \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2}+2 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) d +d^{2}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}"," ",0,"-1/2*e^(3/2)*sum((_R^2+2*_R*d+d^2)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))","C"
364,1,272,249,0.029000," ","int((e*x^2+d)^(1/2)/x^2/(c*x^4+b*x^2+a),x)","\frac{\sqrt{e}\, \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{a}+\frac{\sqrt{e}\, \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{a}+\frac{\sqrt{e}\, \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +c \,d^{3}+2 \left(-2 a \,e^{2}+2 d e b -c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 a \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}+\frac{\sqrt{e \,x^{2}+d}\, e x}{a d}-\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}{a d x}"," ",0,"-1/a/d/x*(e*x^2+d)^(3/2)+1/a*e/d*x*(e*x^2+d)^(1/2)+1/a*e^(1/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))+1/2/a*e^(1/2)*sum((_R^2*c*d+2*(-2*a*e^2+2*b*d*e-c*d^2)*_R+c*d^3)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))+1/a*e^(1/2)*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))","C"
365,1,322,322,0.038000," ","int((e*x^2+d)^(1/2)/x^4/(c*x^4+b*x^2+a),x)","-\frac{b \sqrt{e}\, \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{a^{2}}-\frac{b \sqrt{e}\, \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{a^{2}}-\frac{\sqrt{e \,x^{2}+d}\, b e x}{a^{2} d}+\frac{\sqrt{e}\, \left(a c \,d^{2} e -b c \,d^{3}+\left(a e -b d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c +2 \left(2 a b \,e^{2}+a c d e -2 b^{2} d e +b c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 a^{2} \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} b}{a^{2} d x}-\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}{3 a d \,x^{3}}"," ",0,"1/a^2*b/d/x*(e*x^2+d)^(3/2)-1/a^2*b*e/d*x*(e*x^2+d)^(1/2)-1/a^2*b*e^(1/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))+1/2/a^2*e^(1/2)*sum((c*(a*e-b*d)*_R^2+2*(2*a*b*e^2+a*c*d*e-2*b^2*d*e+b*c*d^2)*_R+a*c*d^2*e-b*c*d^3)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))-1/a^2*e^(1/2)*b*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))-1/3/a/d/x^3*(e*x^2+d)^(3/2)","C"
366,1,503,449,0.038000," ","int((e*x^2+d)^(1/2)/x^6/(c*x^4+b*x^2+a),x)","-\frac{c \sqrt{e}\, \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{a^{2}}-\frac{c \sqrt{e}\, \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{a^{2}}+\frac{b^{2} \sqrt{e}\, \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{a^{3}}+\frac{b^{2} \sqrt{e}\, \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{a^{3}}-\frac{\sqrt{e \,x^{2}+d}\, c e x}{a^{2} d}+\frac{\sqrt{e \,x^{2}+d}\, b^{2} e x}{a^{3} d}-\frac{\sqrt{e}\, \left(a b c \,d^{2} e +a \,c^{2} d^{3}-b^{2} c \,d^{3}+\left(a b e +a c d -b^{2} d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c +2 \left(-2 a^{2} c \,e^{2}+2 a \,b^{2} e^{2}+3 a b c d e -a \,c^{2} d^{2}-2 b^{3} d e +b^{2} c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 a^{3} \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} c}{a^{2} d x}-\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} b^{2}}{a^{3} d x}+\frac{2 \left(e \,x^{2}+d \right)^{\frac{3}{2}} e}{15 a \,d^{2} x^{3}}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} b}{3 a^{2} d \,x^{3}}-\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}{5 a d \,x^{5}}"," ",0,"1/a^2/d/x*(e*x^2+d)^(3/2)*c-1/a^3/d/x*(e*x^2+d)^(3/2)*b^2-1/a^2*e/d*x*(e*x^2+d)^(1/2)*c+1/a^3*e/d*x*(e*x^2+d)^(1/2)*b^2-1/a^2*e^(1/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))*c+1/a^3*e^(1/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))*b^2-1/2/a^3*e^(1/2)*sum((c*(a*b*e+a*c*d-b^2*d)*_R^2+2*(-2*a^2*c*e^2+2*a*b^2*e^2+3*a*b*c*d*e-a*c^2*d^2-2*b^3*d*e+b^2*c*d^2)*_R+a*b*c*d^2*e+a*c^2*d^3-b^2*c*d^3)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))-1/a^2*e^(1/2)*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))*c+1/a^3*e^(1/2)*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))*b^2+1/3/a^2*b/d/x^3*(e*x^2+d)^(3/2)-1/5/a/d/x^5*(e*x^2+d)^(3/2)+2/15/a*e/d^2/x^3*(e*x^2+d)^(3/2)","C"
367,1,490,399,0.033000," ","int(x^3*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x)","-\frac{e^{\frac{3}{2}} x^{3}}{6 c}+\frac{d^{3}}{24 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{3} c}+\frac{\sqrt{e \,x^{2}+d}\, e \,x^{2}}{8 c}+\frac{b \,e^{\frac{3}{2}} x}{2 c^{2}}-\frac{3 d \sqrt{e}\, x}{4 c}-\frac{b d e}{2 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) c^{2}}+\frac{5 d^{2}}{8 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) c}-\frac{\sqrt{e \,x^{2}+d}\, b e}{2 c^{2}}+\frac{5 \sqrt{e \,x^{2}+d}\, d}{8 c}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}}}{24 c}+\frac{\left(a c \,d^{3} e^{2}-b^{2} d^{3} e^{2}+2 b c \,d^{4} e -c^{2} d^{5}+\left(-a c \,e^{2}+b^{2} e^{2}-2 b c d e +c^{2} d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{6}+\left(4 a b \,e^{3}-5 a d \,e^{2} c -3 b^{2} d \,e^{2}+6 b c \,d^{2} e -3 c^{2} d^{3}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{4}+\left(-4 a b \,e^{3}+5 a d \,e^{2} c +3 b^{2} d \,e^{2}-6 b c \,d^{2} e +3 c^{2} d^{3}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{2} d \right) \ln \left(-\sqrt{e}\, x -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)+\sqrt{e \,x^{2}+d}\right)}{4 c^{2} \left(\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{7} c +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} b e -3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} c d +8 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} b d e +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} c \,d^{2}+\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) b \,d^{2} e -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) c \,d^{3}\right)}"," ",0,"-1/6/c*e^(3/2)*x^3+1/8/c*e*(e*x^2+d)^(1/2)*x^2-3/4/c*e^(1/2)*x*d+1/24*(e*x^2+d)^(3/2)/c+1/2/c^2*e^(3/2)*x*b-1/2/c^2*(e*x^2+d)^(1/2)*b*e+5/8/c*(e*x^2+d)^(1/2)*d+1/4/c^2*sum(((-a*c*e^2+b^2*e^2-2*b*c*d*e+c^2*d^2)*_R^6+(4*a*b*e^3-5*a*c*d*e^2-3*b^2*d*e^2+6*b*c*d^2*e-3*c^2*d^3)*_R^4+d*(-4*a*b*e^3+5*a*c*d*e^2+3*b^2*d*e^2-6*b*c*d^2*e+3*c^2*d^3)*_R^2+a*c*d^3*e^2-b^2*d^3*e^2+2*b*c*d^4*e-c^2*d^5)/(_R^7*c+3*_R^5*b*e-3*_R^5*c*d+8*_R^3*a*e^2-4*_R^3*b*d*e+3*_R^3*c*d^2+_R*b*d^2*e-_R*c*d^3)*ln(-e^(1/2)*x-_R+(e*x^2+d)^(1/2)),_R=RootOf(_Z^8*c+(4*b*e-4*c*d)*_Z^6+c*d^4+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^4+(4*b*d^2*e-4*c*d^3)*_Z^2))-1/2/c^2*d/(-e^(1/2)*x+(e*x^2+d)^(1/2))*b*e+5/8/c*d^2/(-e^(1/2)*x+(e*x^2+d)^(1/2))+1/24/c*d^3/(-e^(1/2)*x+(e*x^2+d)^(1/2))^3","C"
368,1,279,278,0.021000," ","int(x*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x)","-\frac{e^{\frac{3}{2}} x}{2 c}+\frac{d e}{2 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) c}+\frac{e \left(\left(-b e +2 c d \right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{6}+b \,d^{3} e -2 c \,d^{4}+\left(-4 a \,e^{2}+3 d e b -2 c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{4}+\left(4 a \,e^{2}-3 d e b +2 c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{2} d \right) \ln \left(-\sqrt{e}\, x -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)+\sqrt{e \,x^{2}+d}\right)}{4 c \left(\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{7} c +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} b e -3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} c d +8 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} b d e +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} c \,d^{2}+\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) b \,d^{2} e -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) c \,d^{3}\right)}+\frac{\sqrt{e \,x^{2}+d}\, e}{2 c}"," ",0,"-1/2*e^(3/2)/c*x+1/2*e*(e*x^2+d)^(1/2)/c+1/4*e/c*sum(((-b*e+2*c*d)*_R^6+(-4*a*e^2+3*b*d*e-2*c*d^2)*_R^4+d*(4*a*e^2-3*b*d*e+2*c*d^2)*_R^2+b*d^3*e-2*c*d^4)/(_R^7*c+3*_R^5*b*e-3*_R^5*c*d+8*_R^3*a*e^2-4*_R^3*b*d*e+3*_R^3*c*d^2+_R*b*d^2*e-_R*c*d^3)*ln(-e^(1/2)*x-_R+(e*x^2+d)^(1/2)),_R=RootOf(_Z^8*c+(4*b*e-4*c*d)*_Z^6+c*d^4+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^4+(4*b*d^2*e-4*c*d^3)*_Z^2))+1/2*e/c*d/(-e^(1/2)*x+(e*x^2+d)^(1/2))","C"
369,1,388,292,0.029000," ","int((e*x^2+d)^(3/2)/x/(c*x^4+b*x^2+a),x)","\frac{e^{\frac{3}{2}} x^{3}}{6 a}-\frac{d^{3}}{24 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{3} a}-\frac{\sqrt{e \,x^{2}+d}\, e \,x^{2}}{8 a}-\frac{d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{e \,x^{2}+d}\, \sqrt{d}}{x}\right)}{a}+\frac{3 d \sqrt{e}\, x}{4 a}-\frac{5 d^{2}}{8 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) a}+\frac{3 \sqrt{e \,x^{2}+d}\, d}{8 a}-\frac{\left(\left(-a \,e^{2}+c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{6}+a \,d^{3} e^{2}-c \,d^{5}+\left(-5 a \,e^{2}+4 d e b -3 c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{4} d +\left(5 a \,e^{2}-4 d e b +3 c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{2} d^{2}\right) \ln \left(-\sqrt{e}\, x -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)+\sqrt{e \,x^{2}+d}\right)}{4 a \left(\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{7} c +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} b e -3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} c d +8 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} b d e +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} c \,d^{2}+\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) b \,d^{2} e -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) c \,d^{3}\right)}+\frac{7 \left(e \,x^{2}+d \right)^{\frac{3}{2}}}{24 a}"," ",0,"7/24/a*(e*x^2+d)^(3/2)-1/a*d^(3/2)*ln((2*d+2*(e*x^2+d)^(1/2)*d^(1/2))/x)+3/8/a*(e*x^2+d)^(1/2)*d+1/6/a*e^(3/2)*x^3-1/8/a*e*(e*x^2+d)^(1/2)*x^2+3/4/a*e^(1/2)*x*d-1/4/a*sum(((-a*e^2+c*d^2)*_R^6+d*(-5*a*e^2+4*b*d*e-3*c*d^2)*_R^4+d^2*(5*a*e^2-4*b*d*e+3*c*d^2)*_R^2+a*d^3*e^2-c*d^5)/(_R^7*c+3*_R^5*b*e-3*_R^5*c*d+8*_R^3*a*e^2-4*_R^3*b*d*e+3*_R^3*c*d^2+_R*b*d^2*e-_R*c*d^3)*ln(-e^(1/2)*x-_R+(e*x^2+d)^(1/2)),_R=RootOf(_Z^8*c+(4*b*e-4*c*d)*_Z^6+c*d^4+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^4+(4*b*d^2*e-4*c*d^3)*_Z^2))-5/8/a*d^2/(-e^(1/2)*x+(e*x^2+d)^(1/2))-1/24/a*d^3/(-e^(1/2)*x+(e*x^2+d)^(1/2))^3","C"
370,1,555,352,0.043000," ","int((e*x^2+d)^(3/2)/x^3/(c*x^4+b*x^2+a),x)","-\frac{b \,e^{\frac{3}{2}} x^{3}}{6 a^{2}}+\frac{b \,d^{3}}{24 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{3} a^{2}}+\frac{\sqrt{e \,x^{2}+d}\, b e \,x^{2}}{8 a^{2}}-\frac{3 \sqrt{d}\, e \ln \left(\frac{2 d +2 \sqrt{e \,x^{2}+d}\, \sqrt{d}}{x}\right)}{2 a}+\frac{e^{\frac{3}{2}} x}{2 a}+\frac{b \,d^{\frac{3}{2}} \ln \left(\frac{2 d +2 \sqrt{e \,x^{2}+d}\, \sqrt{d}}{x}\right)}{a^{2}}-\frac{3 b d \sqrt{e}\, x}{4 a^{2}}-\frac{d e}{2 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) a}+\frac{5 b \,d^{2}}{8 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right) a^{2}}+\frac{\sqrt{e \,x^{2}+d}\, e}{a}-\frac{3 \sqrt{e \,x^{2}+d}\, b d}{8 a^{2}}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} e}{2 a d}-\frac{7 \left(e \,x^{2}+d \right)^{\frac{3}{2}} b}{24 a^{2}}+\frac{\left(\left(-2 a e +b d \right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{6} c d +2 a c \,d^{4} e -b c \,d^{5}+\left(4 a^{2} e^{3}-8 a b d \,e^{2}+2 a c \,d^{2} e +4 b^{2} d^{2} e -3 b c \,d^{3}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{4}+\left(-4 a^{2} e^{3}+8 a b d \,e^{2}-2 a c \,d^{2} e -4 b^{2} d^{2} e +3 b c \,d^{3}\right) \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{2} d \right) \ln \left(-\sqrt{e}\, x -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)+\sqrt{e \,x^{2}+d}\right)}{4 a^{2} \left(\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{7} c +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} b e -3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{5} c d +8 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} b d e +3 \RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right)^{3} c \,d^{2}+\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) b \,d^{2} e -\RootOf \left(\textit{\_Z}^{8} c +\left(4 b e -4 c d \right) \textit{\_Z}^{6}+c \,d^{4}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{4}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z}^{2}\right) c \,d^{3}\right)}-\frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}{2 a d \,x^{2}}"," ",0,"-7/24/a^2*b*(e*x^2+d)^(3/2)+1/a^2*b*d^(3/2)*ln((2*d+2*(e*x^2+d)^(1/2)*d^(1/2))/x)-3/8/a^2*b*(e*x^2+d)^(1/2)*d-1/6/a^2*e^(3/2)*x^3*b+1/8/a^2*e*(e*x^2+d)^(1/2)*x^2*b-3/4/a^2*e^(1/2)*x*b*d+1/2/a*e^(3/2)*x+1/a*(e*x^2+d)^(1/2)*e+1/4/a^2*sum((c*d*(-2*a*e+b*d)*_R^6+(4*a^2*e^3-8*a*b*d*e^2+2*a*c*d^2*e+4*b^2*d^2*e-3*b*c*d^3)*_R^4+d*(-4*a^2*e^3+8*a*b*d*e^2-2*a*c*d^2*e-4*b^2*d^2*e+3*b*c*d^3)*_R^2+2*a*c*d^4*e-b*c*d^5)/(_R^7*c+3*_R^5*b*e-3*_R^5*c*d+8*_R^3*a*e^2-4*_R^3*b*d*e+3*_R^3*c*d^2+_R*b*d^2*e-_R*c*d^3)*ln(-e^(1/2)*x-_R+(e*x^2+d)^(1/2)),_R=RootOf(_Z^8*c+(4*b*e-4*c*d)*_Z^6+c*d^4+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^4+(4*b*d^2*e-4*c*d^3)*_Z^2))-1/2/a*d/(-e^(1/2)*x+(e*x^2+d)^(1/2))*e+5/8/a^2*d^2/(-e^(1/2)*x+(e*x^2+d)^(1/2))*b+1/24/a^2*b*d^3/(-e^(1/2)*x+(e*x^2+d)^(1/2))^3-1/2/a/d/x^2*(e*x^2+d)^(5/2)+1/2/a*e/d*(e*x^2+d)^(3/2)-3/2/a*e*d^(1/2)*ln((2*d+2*(e*x^2+d)^(1/2)*d^(1/2))/x)","C"
371,1,516,513,0.039000," ","int(x^4*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x)","\frac{b \,e^{\frac{3}{2}} x^{2}}{4 c^{2}}+\frac{a \,e^{\frac{3}{2}} \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{c^{2}}-\frac{b^{2} e^{\frac{3}{2}} \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{c^{3}}-\frac{b \,d^{2} \sqrt{e}}{8 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2} c^{2}}+\frac{3 b d \sqrt{e}\, \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{2 c^{2}}+\frac{3 d^{2} \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{8 c \sqrt{e}}-\frac{\sqrt{e \,x^{2}+d}\, b e x}{4 c^{2}}+\frac{3 \sqrt{e \,x^{2}+d}\, d x}{8 c}+\frac{b d \sqrt{e}}{8 c^{2}}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} x}{4 c}-\frac{\sqrt{e}\, \left(2 a b c \,d^{2} e^{2}-2 a \,c^{2} d^{3} e -b^{3} d^{2} e^{2}+2 b^{2} c \,d^{3} e -b \,c^{2} d^{4}+\left(2 a b \,e^{2} c -2 a \,c^{2} d e -b^{3} e^{2}+2 b^{2} d e c -b \,c^{2} d^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2}+2 \left(2 a^{2} c \,e^{3}-2 a \,b^{2} e^{3}+2 a b c d \,e^{2}+b^{3} d \,e^{2}-2 b^{2} d^{2} e c +b \,c^{2} d^{3}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 c^{3} \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}"," ",0,"1/4*x*(e*x^2+d)^(3/2)/c+3/8/c*d*x*(e*x^2+d)^(1/2)+3/8/c*d^2/e^(1/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))+1/4/c^2*e^(3/2)*b*x^2-1/4/c^2*e*b*(e*x^2+d)^(1/2)*x+1/8/c^2*e^(1/2)*b*d-1/2/c^3*e^(1/2)*sum(((2*a*b*c*e^2-2*a*c^2*d*e-b^3*e^2+2*b^2*c*d*e-b*c^2*d^2)*_R^2+2*(2*a^2*c*e^3-2*a*b^2*e^3+2*a*b*c*d*e^2+b^3*d*e^2-2*b^2*c*d^2*e+b*c^2*d^3)*_R+2*a*b*c*d^2*e^2-2*a*c^2*d^3*e-b^3*d^2*e^2+2*b^2*c*d^3*e-b*c^2*d^4)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))+1/c^2*e^(3/2)*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))*a-1/c^3*e^(3/2)*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))*b^2+3/2/c^2*e^(1/2)*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))*b*d-1/8/c^2*e^(1/2)*b*d^2/(-e^(1/2)*x+(e*x^2+d)^(1/2))^2","C"
372,1,382,413,0.033000," ","int(x^2*(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x)","-\frac{e^{\frac{3}{2}} x^{2}}{4 c}+\frac{b \,e^{\frac{3}{2}} \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{c^{2}}+\frac{d^{2} \sqrt{e}}{8 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2} c}-\frac{3 d \sqrt{e}\, \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{2 c}+\frac{\sqrt{e \,x^{2}+d}\, e x}{4 c}-\frac{d \sqrt{e}}{8 c}+\frac{\sqrt{e}\, \left(a c \,d^{2} e^{2}-b^{2} d^{2} e^{2}+2 b c \,d^{3} e -c^{2} d^{4}+\left(a c \,e^{2}-b^{2} e^{2}+2 b c d e -c^{2} d^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2}+2 \left(-2 a b \,e^{3}+3 a d \,e^{2} c +b^{2} d \,e^{2}-2 b c \,d^{2} e +c^{2} d^{3}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 c^{2} \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}"," ",0,"-1/4*e^(3/2)/c*x^2+1/4*e*x*(e*x^2+d)^(1/2)/c-1/8*e^(1/2)/c*d+1/2*e^(1/2)/c^2*sum(((a*c*e^2-b^2*e^2+2*b*c*d*e-c^2*d^2)*_R^2+2*(-2*a*b*e^3+3*a*c*d*e^2+b^2*d*e^2-2*b*c*d^2*e+c^2*d^3)*_R+a*c*d^2*e^2-b^2*d^2*e^2+2*b*c*d^3*e-c^2*d^4)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))+1/8*e^(1/2)/c*d^2/(-e^(1/2)*x+(e*x^2+d)^(1/2))^2+e^(3/2)/c^2*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))*b-3/2*e^(1/2)/c*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))*d","C"
373,1,217,415,0.027000," ","int((e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x)","-\frac{e^{\frac{3}{2}} \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{c}+\frac{e^{\frac{3}{2}} \left(b \,d^{2} e -2 c \,d^{3}+\left(b e -2 c d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2}+2 \left(2 a e -b d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) e \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 c \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}"," ",0,"1/2*e^(3/2)/c*sum(((b*e-2*c*d)*_R^2+2*e*(2*a*e-b*d)*_R+b*d^2*e-2*c*d^3)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))-e^(3/2)/c*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))","C"
374,1,360,218,0.036000," ","int((e*x^2+d)^(3/2)/x^2/(c*x^4+b*x^2+a),x)","\frac{e^{\frac{3}{2}} x^{2}}{4 a}-\frac{d^{2} \sqrt{e}}{8 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2} a}+\frac{3 d \sqrt{e}\, \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{2 a}+\frac{3 d \sqrt{e}\, \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{2 a}+\frac{5 \sqrt{e \,x^{2}+d}\, e x}{4 a}+\frac{d \sqrt{e}}{8 a}-\frac{\sqrt{e}\, \left(a \,d^{2} e^{2}-c \,d^{4}+\left(a \,e^{2}-c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2}+2 \left(3 a \,e^{2}-2 d e b +c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 a \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}+\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} e x}{a d}-\frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}{a d x}"," ",0,"-1/a/d/x*(e*x^2+d)^(5/2)+1/a*e/d*x*(e*x^2+d)^(3/2)+5/4/a*e*x*(e*x^2+d)^(1/2)+3/2/a*e^(1/2)*d*ln(e^(1/2)*x+(e*x^2+d)^(1/2))+1/4/a*e^(3/2)*x^2+1/8/a*e^(1/2)*d-1/2/a*e^(1/2)*sum(((a*e^2-c*d^2)*_R^2+2*d*(3*a*e^2-2*b*d*e+c*d^2)*_R+a*d^2*e^2-c*d^4)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))-1/8/a*e^(1/2)*d^2/(-e^(1/2)*x+(e*x^2+d)^(1/2))^2+3/2/a*e^(1/2)*d*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))","C"
375,1,511,445,0.036000," ","int((e*x^2+d)^(3/2)/x^4/(c*x^4+b*x^2+a),x)","-\frac{b \,e^{\frac{3}{2}} x^{2}}{4 a^{2}}+\frac{e^{\frac{3}{2}} \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{a}+\frac{e^{\frac{3}{2}} \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{a}+\frac{b \,d^{2} \sqrt{e}}{8 \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2} a^{2}}-\frac{3 b d \sqrt{e}\, \ln \left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{2 a^{2}}-\frac{3 b d \sqrt{e}\, \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{2 a^{2}}+\frac{\sqrt{e \,x^{2}+d}\, e^{2} x}{a d}-\frac{5 \sqrt{e \,x^{2}+d}\, b e x}{4 a^{2}}-\frac{b d \sqrt{e}}{8 a^{2}}+\frac{2 \left(e \,x^{2}+d \right)^{\frac{3}{2}} e^{2} x}{3 a \,d^{2}}-\frac{\left(e \,x^{2}+d \right)^{\frac{3}{2}} b e x}{a^{2} d}+\frac{\sqrt{e}\, \left(2 a c \,d^{3} e -b c \,d^{4}+\left(2 a e -b d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +2 \left(-2 a^{2} e^{3}+4 a b d \,e^{2}-2 b^{2} d^{2} e +b c \,d^{3}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 a^{2} \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}-\frac{2 \left(e \,x^{2}+d \right)^{\frac{5}{2}} e}{3 a \,d^{2} x}+\frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}} b}{a^{2} d x}-\frac{\left(e \,x^{2}+d \right)^{\frac{5}{2}}}{3 a d \,x^{3}}"," ",0,"1/a^2*b/d/x*(e*x^2+d)^(5/2)-1/a^2*b*e/d*x*(e*x^2+d)^(3/2)-5/4/a^2*b*e*x*(e*x^2+d)^(1/2)-3/2/a^2*b*e^(1/2)*d*ln(e^(1/2)*x+(e*x^2+d)^(1/2))-1/4/a^2*e^(3/2)*x^2*b-1/8/a^2*e^(1/2)*b*d+1/2/a^2*e^(1/2)*sum((c*d*(2*a*e-b*d)*_R^2+2*(-2*a^2*e^3+4*a*b*d*e^2-2*b^2*d^2*e+b*c*d^3)*_R+2*a*c*d^3*e-b*c*d^4)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))+1/a*e^(3/2)*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))-3/2/a^2*e^(1/2)*ln(-e^(1/2)*x+(e*x^2+d)^(1/2))*b*d+1/8/a^2*e^(1/2)*b*d^2/(-e^(1/2)*x+(e*x^2+d)^(1/2))^2-1/3/a/d/x^3*(e*x^2+d)^(5/2)-2/3/a*e/d^2/x*(e*x^2+d)^(5/2)+2/3/a*e^2/d^2*x*(e*x^2+d)^(3/2)+1/a*e^2/d*x*(e*x^2+d)^(1/2)+1/a*e^(3/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))","C"
376,1,2134,239,0.099000," ","int(x^5*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x)","\frac{8 a^{2} b \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, c}-\frac{8 a^{2} b \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, c}+\frac{8 a^{2} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{8 a^{2} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{2 a \,b^{3} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, c^{2}}+\frac{2 a \,b^{3} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, c^{2}}-\frac{2 a \,b^{2} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, c}+\frac{2 a \,b^{2} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, c}+\frac{4 \sqrt{-4 a c +b^{2}}\, a^{2} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, c}+\frac{4 \sqrt{-4 a c +b^{2}}\, a^{2} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, c}-\frac{2 \sqrt{-4 a c +b^{2}}\, a \,b^{2} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, c^{2}}-\frac{2 \sqrt{-4 a c +b^{2}}\, a \,b^{2} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, c^{2}}-\frac{2 \sqrt{-4 a c +b^{2}}\, a b \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, c}-\frac{2 \sqrt{-4 a c +b^{2}}\, a b \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, c}-\frac{2 b}{\left(\frac{2}{x^{2}}-\frac{2 \sqrt{-x^{2}+1}}{x^{2}}\right) c^{2}}-\frac{\left(-x^{2}+1\right)^{\frac{3}{2}}}{3 c}"," ",0,"-1/3*(-x^2+1)^(3/2)/c+4/c*a^2/(8*a*c-2*b^2)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(-2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)-2*a-2*b)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))*(-4*a*c+b^2)^(1/2)-2/c^2*a/(8*a*c-2*b^2)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(-2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)-2*a-2*b)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))*b^2*(-4*a*c+b^2)^(1/2)-2/c*a/(8*a*c-2*b^2)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(-2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)-2*a-2*b)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))*(-4*a*c+b^2)^(1/2)*b+8/c*a^2/(8*a*c-2*b^2)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(-2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)-2*a-2*b)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))*b+8*a^2/(8*a*c-2*b^2)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(-2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)-2*a-2*b)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))-2/c^2*a/(8*a*c-2*b^2)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(-2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)-2*a-2*b)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))*b^3-2/c*a/(8*a*c-2*b^2)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(-2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)-2*a-2*b)/(4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))*b^2+4/c*a^2/(8*a*c-2*b^2)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)+2*a+2*b)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))*(-4*a*c+b^2)^(1/2)-2/c^2*a/(8*a*c-2*b^2)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)+2*a+2*b)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))*b^2*(-4*a*c+b^2)^(1/2)-2/c*a/(8*a*c-2*b^2)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)+2*a+2*b)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))*(-4*a*c+b^2)^(1/2)*b-8/c*a^2/(8*a*c-2*b^2)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)+2*a+2*b)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))*b-8*a^2/(8*a*c-2*b^2)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)+2*a+2*b)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))+2/c^2*a/(8*a*c-2*b^2)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)+2*a+2*b)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))*b^3+2/c*a/(8*a*c-2*b^2)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2)*arctan(1/2*(2*((-x^2+1)^(1/2)-1)^2/x^2*a+2*(-4*a*c+b^2)^(1/2)+2*a+2*b)/(4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*b*(-4*a*c+b^2)^(1/2)-2*a*b)^(1/2))*b^2-2/c^2*b/(2/x^2-2/x^2*(-x^2+1)^(1/2))","B"
377,1,1223,189,0.063000," ","int(x^3*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x)","-\frac{8 a^{2} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{8 a^{2} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{2 a \,b^{2} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, c}-\frac{2 a \,b^{2} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, c}+\frac{2 \sqrt{-4 a c +b^{2}}\, a b \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, c}+\frac{2 \sqrt{-4 a c +b^{2}}\, a b \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, c}+\frac{4 \sqrt{-4 a c +b^{2}}\, a \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{4 \sqrt{-4 a c +b^{2}}\, a \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(8 a c -2 b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{2}{\left(\frac{-x^{2}+1}{x^{2}}-\frac{2 \sqrt{-x^{2}+1}}{x^{2}}+\frac{1}{x^{2}}+1\right) c}"," ",0,"2/(8*a*c-2*b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*(-4*a*c+b^2)^(1/2)*a*b/c*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))+4*a/(8*a*c-2*b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*(-4*a*c+b^2)^(1/2)-8/(8*a*c-2*b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*a^2*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))+2/(8*a*c-2*b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*a*b^2/c*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))+2/(8*a*c-2*b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*(-4*a*c+b^2)^(1/2)*a*b/c*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))+4*a/(8*a*c-2*b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*(-4*a*c+b^2)^(1/2)+8/(8*a*c-2*b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*a^2*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))-2/(8*a*c-2*b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*a*b^2/c*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))+2/c/(1/x^2*(-x^2+1)-2*(-x^2+1)^(1/2)/x^2+1/x^2+1)","B"
378,1,1167,143,0.051000," ","int(x*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x)","-\frac{4 a c \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{4 a c \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{b^{2} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{b^{2} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{2 \sqrt{-4 a c +b^{2}}\, a \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{2 \sqrt{-4 a c +b^{2}}\, a \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{\sqrt{-4 a c +b^{2}}\, b \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{\sqrt{-4 a c +b^{2}}\, b \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}"," ",0,"-2*a/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*(-4*a*c+b^2)^(1/2)-1/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*(-4*a*c+b^2)^(1/2)*b-4*a/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*c+1/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b^2-2*a/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*(-4*a*c+b^2)^(1/2)-1/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*(-4*a*c+b^2)^(1/2)*b+4*a/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*c-1/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b^2","B"
379,1,2099,196,0.064000," ","int((-x^2+1)^(1/2)/x/(c*x^4+b*x^2+a),x)","\frac{4 a c \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{4 a c \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{b^{3} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, a}+\frac{b^{3} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, a}-\frac{b^{2} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{b^{2} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{4 b c \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{4 b c \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{\sqrt{-4 a c +b^{2}}\, b^{2} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, a}+\frac{\sqrt{-4 a c +b^{2}}\, b^{2} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, a}+\frac{\sqrt{-4 a c +b^{2}}\, b \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{\sqrt{-4 a c +b^{2}}\, b \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{2 \sqrt{-4 a c +b^{2}}\, c \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{2 \sqrt{-4 a c +b^{2}}\, c \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{\arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)}{a}+\frac{\sqrt{-x^{2}+1}}{a}-\frac{2}{\left(\frac{2}{x^{2}}-\frac{2 \sqrt{-x^{2}+1}}{x^{2}}\right) a}"," ",0,"1/a*(-x^2+1)^(1/2)-1/a*arctanh(1/(-x^2+1)^(1/2))+1/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*(-4*a*c+b^2)^(1/2)*b*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))-2/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*c*(-4*a*c+b^2)^(1/2)+1/a/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b^2*(-4*a*c+b^2)^(1/2)+4/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*a*c*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))-1/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*b^2*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))+4/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b*c-1/a/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b^3+1/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*(-4*a*c+b^2)^(1/2)*b*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))-2/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*c*(-4*a*c+b^2)^(1/2)+1/a/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b^2*(-4*a*c+b^2)^(1/2)-4/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*a*c*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))+1/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*b^2*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))-4/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b*c+1/a/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b^3-2/a/(2/x^2-2*(-x^2+1)^(1/2)/x^2)","B"
380,1,2770,240,0.085000," ","int((-x^2+1)^(1/2)/x^3/(c*x^4+b*x^2+a),x)","\frac{b^{3} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, a}-\frac{b^{3} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, a}-\frac{5 b^{2} c \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, a}+\frac{5 b^{2} c \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, a}+\frac{b^{4} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, a^{2}}-\frac{b^{4} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, a^{2}}-\frac{4 b c \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{4 b c \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{4 c^{2} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{4 c^{2} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}-\frac{\sqrt{-4 a c +b^{2}}\, b^{2} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, a}-\frac{\sqrt{-4 a c +b^{2}}\, b^{2} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, a}+\frac{3 \sqrt{-4 a c +b^{2}}\, b c \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, a}+\frac{3 \sqrt{-4 a c +b^{2}}\, b c \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, a}-\frac{\sqrt{-4 a c +b^{2}}\, b^{3} \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}\, a^{2}}-\frac{\sqrt{-4 a c +b^{2}}\, b^{3} \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}\, a^{2}}+\frac{2 \sqrt{-4 a c +b^{2}}\, c \arctan \left(\frac{-2 a -2 b -\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}+2 \sqrt{-4 a c +b^{2}}\, a +2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{2 \sqrt{-4 a c +b^{2}}\, c \arctan \left(\frac{2 a +2 b +\frac{2 \left(\sqrt{-x^{2}+1}-1\right)^{2} a}{x^{2}}+2 \sqrt{-4 a c +b^{2}}}{2 \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-2 a b +4 a c -2 b^{2}-2 \sqrt{-4 a c +b^{2}}\, a -2 \sqrt{-4 a c +b^{2}}\, b}}+\frac{\arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)}{2 a}+\frac{b \arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)}{a^{2}}-\frac{\sqrt{-x^{2}+1}}{2 a}-\frac{\sqrt{-x^{2}+1}\, b}{a^{2}}+\frac{2 b}{\left(\frac{2}{x^{2}}-\frac{2 \sqrt{-x^{2}+1}}{x^{2}}\right) a^{2}}-\frac{\left(-x^{2}+1\right)^{\frac{3}{2}}}{2 a \,x^{2}}"," ",0,"-1/a^2*b*(-x^2+1)^(1/2)+1/a^2*b*arctanh(1/(-x^2+1)^(1/2))+2/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*(-4*a*c+b^2)^(1/2)*c*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))-1/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*(-4*a*c+b^2)^(1/2)/a*b^2*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))+3/a/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b*c*(-4*a*c+b^2)^(1/2)-1/a^2/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b^3*(-4*a*c+b^2)^(1/2)-4/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*b*c*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))+4/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*c^2+1/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)/a*b^3*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))-5/a/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b^2*c+1/a^2/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(-2*a-2*b-2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2+2*(-4*a*c+b^2)^(1/2)*a+2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b^4+2/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*(-4*a*c+b^2)^(1/2)*c*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))-1/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*(-4*a*c+b^2)^(1/2)/a*b^2*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))+3/a/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b*c*(-4*a*c+b^2)^(1/2)-1/a^2/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b^3*(-4*a*c+b^2)^(1/2)+4/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*b*c*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))-4/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*c^2-1/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)/a*b^3*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))+5/a/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b^2*c-1/a^2/(4*a*c-b^2)/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2)*arctan(1/2*(2*a+2*b+2*((-x^2+1)^(1/2)-1)^2*a/x^2+2*(-4*a*c+b^2)^(1/2))/(-2*a*b+4*a*c-2*b^2-2*(-4*a*c+b^2)^(1/2)*a-2*(-4*a*c+b^2)^(1/2)*b)^(1/2))*b^4+2/a^2*b/(2/x^2-2*(-x^2+1)^(1/2)/x^2)-1/2/a/x^2*(-x^2+1)^(3/2)-1/2*(-x^2+1)^(1/2)/a+1/2/a*arctanh(1/(-x^2+1)^(1/2))","B"
381,1,222,281,0.042000," ","int(x^4*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x)","-\frac{2 b \arctan \left(\frac{\sqrt{-x^{2}+1}-1}{x}\right)}{c^{2}}+\frac{\sqrt{-x^{2}+1}\, x}{2 c}+\frac{\arcsin \left(x \right)}{2 c}+\frac{\left(\left(b +c \right) \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{6} a +\left(3 a b -a c +4 b^{2}+4 b c \right) \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{4}+\left(3 a b -a c +4 b^{2}+4 b c \right) \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{2}+a b +a c \right) \ln \left(-\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)+\frac{\sqrt{-x^{2}+1}-1}{x}\right)}{4 c^{2} \left(\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{7} a +3 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{5} a +3 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{5} b +3 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{3} a +4 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{3} b +8 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{3} c +\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right) a +\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right) b \right)}"," ",0,"1/2*x*(-x^2+1)^(1/2)/c+1/2*arcsin(x)/c+1/4/c^2*sum((a*(b+c)*_R^6+(3*a*b-a*c+4*b^2+4*b*c)*_R^4+(3*a*b-a*c+4*b^2+4*b*c)*_R^2+a*b+a*c)/(_R^7*a+3*_R^5*a+3*_R^5*b+3*_R^3*a+4*_R^3*b+8*_R^3*c+_R*a+_R*b)*ln(((-x^2+1)^(1/2)-1)/x-_R),_R=RootOf(a*_Z^8+(4*a+4*b)*_Z^6+(6*a+8*b+16*c)*_Z^4+(4*a+4*b)*_Z^2+a))-2/c^2*b*arctan(((-x^2+1)^(1/2)-1)/x)","C"
382,1,175,225,0.023000," ","int(x^2*(-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x)","\frac{2 \arctan \left(\frac{\sqrt{-x^{2}+1}-1}{x}\right)}{c}-\frac{\left(\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{6} a +\left(3 a +4 b +4 c \right) \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{4}+\left(3 a +4 b +4 c \right) \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{2}+a \right) \ln \left(-\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)+\frac{\sqrt{-x^{2}+1}-1}{x}\right)}{4 c \left(\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{7} a +3 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{5} a +3 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{5} b +3 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{3} a +4 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{3} b +8 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{3} c +\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right) a +\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right) b \right)}"," ",0,"-1/4/c*sum((_R^6*a+(4*c+3*a+4*b)*_R^4+(4*c+3*a+4*b)*_R^2+a)/(_R^7*a+3*_R^5*a+3*_R^5*b+3*_R^3*a+4*_R^3*b+8*_R^3*c+_R*a+_R*b)*ln(-_R+((-x^2+1)^(1/2)-1)/x),_R=RootOf(_Z^8*a+(4*a+4*b)*_Z^6+(6*a+8*b+16*c)*_Z^4+(4*a+4*b)*_Z^2+a))+2/c*arctan(((-x^2+1)^(1/2)-1)/x)","C"
383,1,130,180,0.013000," ","int((-x^2+1)^(1/2)/(c*x^4+b*x^2+a),x)","-\frac{\left(\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{6}-\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{4}-\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{2}+1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)+\frac{\sqrt{-x^{2}+1}-1}{x}\right)}{4 \left(\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{7} a +3 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{5} a +3 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{5} b +3 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{3} a +4 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{3} b +8 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{3} c +\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right) a +\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right) b \right)}"," ",0,"-1/4*sum((_R^6-_R^4-_R^2+1)/(_R^7*a+3*_R^5*a+3*_R^5*b+3*_R^3*a+4*_R^3*b+8*_R^3*c+_R*a+_R*b)*ln(-_R+((-x^2+1)^(1/2)-1)/x),_R=RootOf(_Z^8*a+(4*a+4*b)*_Z^6+(6*a+8*b+16*c)*_Z^4+(4*a+4*b)*_Z^2+a))","C"
384,1,217,224,0.027000," ","int((-x^2+1)^(1/2)/x^2/(c*x^4+b*x^2+a),x)","-\frac{\sqrt{-x^{2}+1}\, x}{a}-\frac{\arcsin \left(x \right)}{a}-\frac{2 \arctan \left(\frac{\sqrt{-x^{2}+1}-1}{x}\right)}{a}+\frac{\left(\left(a +b \right) \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{6}+\left(3 a +3 b +4 c \right) \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{4}+\left(3 a +3 b +4 c \right) \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{2}+a +b \right) \ln \left(-\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)+\frac{\sqrt{-x^{2}+1}-1}{x}\right)}{4 a \left(\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{7} a +3 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{5} a +3 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{5} b +3 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{3} a +4 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{3} b +8 \RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right)^{3} c +\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right) a +\RootOf \left(\textit{\_Z}^{8} a +\left(4 a +4 b \right) \textit{\_Z}^{6}+\left(6 a +8 b +16 c \right) \textit{\_Z}^{4}+\left(4 a +4 b \right) \textit{\_Z}^{2}+a \right) b \right)}-\frac{\left(-x^{2}+1\right)^{\frac{3}{2}}}{a x}"," ",0,"-1/a/x*(-x^2+1)^(3/2)-1/a*x*(-x^2+1)^(1/2)-1/a*arcsin(x)+1/4/a*sum(((a+b)*_R^6+(3*a+3*b+4*c)*_R^4+(3*a+3*b+4*c)*_R^2+a+b)/(_R^7*a+3*_R^5*a+3*_R^5*b+3*_R^3*a+4*_R^3*b+8*_R^3*c+_R*a+_R*b)*ln(-_R+((-x^2+1)^(1/2)-1)/x),_R=RootOf(_Z^8*a+(4*a+4*b)*_Z^6+(6*a+8*b+16*c)*_Z^4+(4*a+4*b)*_Z^2+a))-2/a*arctan(((-x^2+1)^(1/2)-1)/x)","C"
385,1,160,71,0.088000," ","int(x^2*(-x^2+1)^(1/2)/(x^4+x^2-1),x)","-\frac{\sqrt{5}\, \arctanh \left(\frac{\sqrt{-x^{2}+1}-1}{\sqrt{2+\sqrt{5}}\, x}\right)}{5 \sqrt{2+\sqrt{5}}}+\frac{\sqrt{\sqrt{5}-2}\, \sqrt{5}\, \arctanh \left(\frac{\sqrt{-x^{2}+1}-1}{\sqrt{\sqrt{5}-2}\, x}\right)}{5}+2 \arctan \left(\frac{\sqrt{-x^{2}+1}-1}{x}\right)-\frac{\sqrt{2+\sqrt{5}}\, \sqrt{5}\, \arctan \left(\frac{\sqrt{-x^{2}+1}-1}{\sqrt{2+\sqrt{5}}\, x}\right)}{5}-\frac{\sqrt{5}\, \arctan \left(\frac{\sqrt{-x^{2}+1}-1}{\sqrt{\sqrt{5}-2}\, x}\right)}{5 \sqrt{\sqrt{5}-2}}"," ",0,"-1/5*(2+5^(1/2))^(1/2)*5^(1/2)*arctan(((-x^2+1)^(1/2)-1)/x/(2+5^(1/2))^(1/2))+1/5*(5^(1/2)-2)^(1/2)*5^(1/2)*arctanh(((-x^2+1)^(1/2)-1)/x/(5^(1/2)-2)^(1/2))-1/5*5^(1/2)/(2+5^(1/2))^(1/2)*arctanh(((-x^2+1)^(1/2)-1)/x/(2+5^(1/2))^(1/2))-1/5*5^(1/2)/(5^(1/2)-2)^(1/2)*arctan(((-x^2+1)^(1/2)-1)/x/(5^(1/2)-2)^(1/2))+2*arctan(((-x^2+1)^(1/2)-1)/x)","B"
386,1,377,406,0.034000," ","int(x^8/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x)","\frac{\sqrt{e \,x^{2}+d}\, x^{3}}{4 c e}-\frac{a \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{c^{2} \sqrt{e}}+\frac{b^{2} \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{c^{3} \sqrt{e}}+\frac{b d \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{2 c^{2} e^{\frac{3}{2}}}+\frac{3 d^{2} \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{8 c \,e^{\frac{5}{2}}}-\frac{\sqrt{e \,x^{2}+d}\, b x}{2 c^{2} e}-\frac{3 \sqrt{e \,x^{2}+d}\, d x}{8 c \,e^{2}}-\frac{\sqrt{e}\, \left(2 a b c \,d^{2}-b^{3} d^{2}+\left(2 a c -b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b +2 \left(2 a^{2} c e -2 a \,b^{2} e -2 a b c d +b^{3} d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 c^{3} \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}"," ",0,"1/4*x^3*(e*x^2+d)^(1/2)/c/e-3/8*d*x*(e*x^2+d)^(1/2)/c/e^2+3/8/c*d^2/e^(5/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))-1/2*b*x*(e*x^2+d)^(1/2)/c^2/e+1/2/c^2*b*d/e^(3/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))-1/c^2*a*ln(e^(1/2)*x+(e*x^2+d)^(1/2))/e^(1/2)+1/c^3*b^2*ln(e^(1/2)*x+(e*x^2+d)^(1/2))/e^(1/2)-1/2/c^3*e^(1/2)*sum((b*(2*a*c-b^2)*_R^2+2*(2*a^2*c*e-2*a*b^2*e-2*a*b*c*d+b^3*d)*_R+2*a*b*c*d^2-b^3*d^2)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))","C"
387,1,269,308,0.026000," ","int(x^6/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x)","-\frac{b \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{c^{2} \sqrt{e}}-\frac{d \ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{2 c \,e^{\frac{3}{2}}}+\frac{\sqrt{e}\, \left(a c \,d^{2}-b^{2} d^{2}+\left(a c -b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2}+2 \left(-2 a b e -a c d +b^{2} d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 c^{2} \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}+\frac{\sqrt{e \,x^{2}+d}\, x}{2 c e}"," ",0,"1/2*x*(e*x^2+d)^(1/2)/c/e-1/2/c*d/e^(3/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))-1/c^2*b*ln(e^(1/2)*x+(e*x^2+d)^(1/2))/e^(1/2)+1/2/c^2*e^(1/2)*sum(((a*c-b^2)*_R^2+2*(-2*a*b*e-a*c*d+b^2*d)*_R+a*c*d^2-b^2*d^2)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))","C"
388,1,200,253,0.022000," ","int(x^4/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x)","\frac{\sqrt{e}\, \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b +b \,d^{2}+2 \left(2 a e -b d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 c \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}+\frac{\ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{c \sqrt{e}}"," ",0,"1/c*ln(e^(1/2)*x+(e*x^2+d)^(1/2))/e^(1/2)+1/2/c*e^(1/2)*sum((_R^2*b+2*(2*a*e-b*d)*_R+b*d^2)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))","C"
389,1,161,200,0.017000," ","int(x^2/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x)","-\frac{\sqrt{e}\, \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2}-2 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) d +d^{2}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}"," ",0,"-1/2*e^(1/2)*sum((_R^2-2*_R*d+d^2)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))","C"
390,1,151,203,0.016000," ","int(1/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x)","-\frac{2 e^{\frac{3}{2}} \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}}"," ",0,"-2*e^(3/2)*sum(_R/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))","C"
391,1,197,238,0.025000," ","int(1/x^2/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x)","\frac{\sqrt{e}\, \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c +c \,d^{2}+2 \left(2 b e -c d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 a \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}-\frac{\sqrt{e \,x^{2}+d}}{a d x}"," ",0,"-(e*x^2+d)^(1/2)/a/d/x+1/2/a*e^(1/2)*sum((c*_R^2+2*(2*b*e-c*d)*_R+c*d^2)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))","C"
392,1,248,292,0.029000," ","int(1/x^4/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x)","-\frac{\sqrt{e}\, \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b c +b c \,d^{2}+2 \left(-2 a c e +2 b^{2} e -b c d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 a^{2} \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}+\frac{2 \sqrt{e \,x^{2}+d}\, e}{3 a \,d^{2} x}+\frac{\sqrt{e \,x^{2}+d}\, b}{a^{2} d x}-\frac{\sqrt{e \,x^{2}+d}}{3 a d \,x^{3}}"," ",0,"b*(e*x^2+d)^(1/2)/a^2/d/x-1/2/a^2*e^(1/2)*sum((b*c*_R^2+2*(-2*a*c*e+2*b^2*e-b*c*d)*_R+b*c*d^2)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))-1/3*(e*x^2+d)^(1/2)/a/d/x^3+2/3*e*(e*x^2+d)^(1/2)/a/d^2/x","C"
393,1,350,381,0.036000," ","int(1/x^6/(c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x)","-\frac{\sqrt{e}\, \left(a \,c^{2} d^{2}-b^{2} c \,d^{2}+\left(a c -b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c +2 \left(4 a b c e -a \,c^{2} d -2 b^{3} e +b^{2} c d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{2 a^{3} \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}-\frac{8 \sqrt{e \,x^{2}+d}\, e^{2}}{15 a \,d^{3} x}-\frac{2 \sqrt{e \,x^{2}+d}\, b e}{3 a^{2} d^{2} x}+\frac{4 \sqrt{e \,x^{2}+d}\, e}{15 a \,d^{2} x^{3}}+\frac{\sqrt{e \,x^{2}+d}\, b}{3 a^{2} d \,x^{3}}-\frac{\left(-a c +b^{2}\right) \sqrt{e \,x^{2}+d}}{a^{3} d x}-\frac{\sqrt{e \,x^{2}+d}}{5 a d \,x^{5}}"," ",0,"-(-a*c+b^2)*(e*x^2+d)^(1/2)/a^3/d/x-1/2/a^3*e^(1/2)*sum((c*(a*c-b^2)*_R^2+2*(4*a*b*c*e-a*c^2*d-2*b^3*e+b^2*c*d)*_R+a*c^2*d^2-b^2*c*d^2)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))+1/3*b*(e*x^2+d)^(1/2)/a^2/d/x^3-2/3*b*e*(e*x^2+d)^(1/2)/a^2/d^2/x-1/5*(e*x^2+d)^(1/2)/a/d/x^5+4/15*e*(e*x^2+d)^(1/2)/a/d^2/x^3-8/15*e^2*(e*x^2+d)^(1/2)/a/d^3/x","C"
394,1,480,302,0.040000," ","int(x^6/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x)","\frac{8 a b \,e^{\frac{3}{2}}}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) \left(2 e \,x^{2}-2 \sqrt{e \,x^{2}+d}\, \sqrt{e}\, x +2 d \right) c^{2}}+\frac{8 a d \sqrt{e}}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) \left(2 e \,x^{2}-2 \sqrt{e \,x^{2}+d}\, \sqrt{e}\, x +2 d \right) c}-\frac{8 b^{2} d \sqrt{e}}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) \left(2 e \,x^{2}-2 \sqrt{e \,x^{2}+d}\, \sqrt{e}\, x +2 d \right) c^{2}}+\frac{2 \sqrt{e}\, \left(a b \,d^{2} e +a c \,d^{3}-b^{2} d^{3}+\left(a b e +a c d -b^{2} d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2}+2 \left(2 a^{2} e^{2}-3 a b d e -a c \,d^{2}+b^{2} d^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) c \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}-\frac{b x}{\sqrt{e \,x^{2}+d}\, c^{2} d}-\frac{x}{\sqrt{e \,x^{2}+d}\, c e}+\frac{\ln \left(\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)}{c \,e^{\frac{3}{2}}}"," ",0,"-1/c*x/e/(e*x^2+d)^(1/2)+1/c/e^(3/2)*ln(e^(1/2)*x+(e*x^2+d)^(1/2))-1/c^2*b*x/d/(e*x^2+d)^(1/2)+2/c*e^(1/2)/(4*a*e^2-4*b*d*e+4*c*d^2)*sum(((a*b*e+a*c*d-b^2*d)*_R^2+2*(2*a^2*e^2-3*a*b*d*e-a*c*d^2+b^2*d^2)*_R+a*b*d^2*e+a*c*d^3-b^2*d^3)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))+8/c^2*e^(3/2)/(4*a*e^2-4*b*d*e+4*c*d^2)/(2*e*x^2-2*e^(1/2)*(e*x^2+d)^(1/2)*x+2*d)*a*b+8/c*e^(1/2)/(4*a*e^2-4*b*d*e+4*c*d^2)/(2*e*x^2-2*e^(1/2)*(e*x^2+d)^(1/2)*x+2*d)*a*d-8/c^2*e^(1/2)/(4*a*e^2-4*b*d*e+4*c*d^2)/(2*e*x^2-2*e^(1/2)*(e*x^2+d)^(1/2)*x+2*d)*b^2*d","C"
395,1,338,317,0.034000," ","int(x^4/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x)","-\frac{8 a \,e^{\frac{3}{2}}}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) \left(2 e \,x^{2}-2 \sqrt{e \,x^{2}+d}\, \sqrt{e}\, x +2 d \right) c}+\frac{8 b d \sqrt{e}}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) \left(2 e \,x^{2}-2 \sqrt{e \,x^{2}+d}\, \sqrt{e}\, x +2 d \right) c}-\frac{2 \sqrt{e}\, \left(a \,d^{2} e -b \,d^{3}+\left(a e -b d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2}+2 \left(-3 a e +b d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}+\frac{x}{\sqrt{e \,x^{2}+d}\, c d}"," ",0,"1/c*x/d/(e*x^2+d)^(1/2)-2*e^(1/2)/(4*a*e^2-4*b*d*e+4*c*d^2)*sum(((a*e-b*d)*_R^2+2*d*(-3*a*e+b*d)*_R+a*d^2*e-b*d^3)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))-8/c*e^(3/2)/(4*a*e^2-4*b*d*e+4*c*d^2)/(2*e*x^2-2*(e*x^2+d)^(1/2)*e^(1/2)*x+2*d)*a+8/c*e^(1/2)/(4*a*e^2-4*b*d*e+4*c*d^2)/(2*e*x^2-2*(e*x^2+d)^(1/2)*e^(1/2)*x+2*d)*b*d","C"
396,1,252,291,0.029000," ","int(x^2/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x)","-\frac{8 d \sqrt{e}}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) \left(2 e \,x^{2}-2 \sqrt{e \,x^{2}+d}\, \sqrt{e}\, x +2 d \right)}-\frac{2 \sqrt{e}\, \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +c \,d^{3}+2 \left(2 a \,e^{2}-c \,d^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}"," ",0,"-2*e^(1/2)/(4*a*e^2-4*b*d*e+4*c*d^2)*sum((_R^2*c*d+2*(2*a*e^2-c*d^2)*_R+c*d^3)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))-8*e^(1/2)*d/(4*a*e^2-4*b*d*e+4*c*d^2)/(2*e*x^2-2*(e*x^2+d)^(1/2)*e^(1/2)*x+2*d)","C"
397,1,246,297,0.024000," ","int(1/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x)","\frac{8 e^{\frac{3}{2}} \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c +c \,d^{2}+2 \left(2 b e -3 c d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{\left(16 a \,e^{2}-16 d e b +16 c \,d^{2}\right) \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}+\frac{32 e^{\frac{3}{2}}}{\left(16 a \,e^{2}-16 d e b +16 c \,d^{2}\right) \left(2 e \,x^{2}-2 \sqrt{e \,x^{2}+d}\, \sqrt{e}\, x +2 d \right)}"," ",0,"8*e^(3/2)/(16*a*e^2-16*b*d*e+16*c*d^2)*sum((_R^2*c+2*(2*b*e-3*c*d)*_R+c*d^2)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))+32*e^(3/2)/(16*a*e^2-16*b*d*e+16*c*d^2)/(2*e*x^2-2*(e*x^2+d)^(1/2)*e^(1/2)*x+2*d)","C"
398,1,387,295,0.037000," ","int(1/x^2/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x)","-\frac{8 b \,e^{\frac{3}{2}}}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) \left(2 e \,x^{2}-2 \sqrt{e \,x^{2}+d}\, \sqrt{e}\, x +2 d \right) a}+\frac{8 c d \sqrt{e}}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) \left(2 e \,x^{2}-2 \sqrt{e \,x^{2}+d}\, \sqrt{e}\, x +2 d \right) a}-\frac{2 \sqrt{e}\, \left(b c \,d^{2} e -c^{2} d^{3}+\left(b e -c d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c +2 \left(-2 a c \,e^{2}+2 b^{2} e^{2}-3 b c d e +c^{2} d^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) a \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}-\frac{2 e x}{\sqrt{e \,x^{2}+d}\, a \,d^{2}}-\frac{1}{\sqrt{e \,x^{2}+d}\, a d x}"," ",0,"-1/a/d/x/(e*x^2+d)^(1/2)-2/a*e/d^2*x/(e*x^2+d)^(1/2)-2/a*e^(1/2)/(4*a*e^2-4*b*d*e+4*c*d^2)*sum((c*(b*e-c*d)*_R^2+2*(-2*a*c*e^2+2*b^2*e^2-3*b*c*d*e+c^2*d^2)*_R+b*c*d^2*e-c^2*d^3)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))-8/a*e^(3/2)/(4*a*e^2-4*b*d*e+4*c*d^2)/(2*e*x^2-2*(e*x^2+d)^(1/2)*e^(1/2)*x+2*d)*b+8/a*e^(1/2)/(4*a*e^2-4*b*d*e+4*c*d^2)/(2*e*x^2-2*(e*x^2+d)^(1/2)*e^(1/2)*x+2*d)*c*d","C"
399,1,541,366,0.042000," ","int(1/x^4/(e*x^2+d)^(3/2)/(c*x^4+b*x^2+a),x)","-\frac{8 c \,e^{\frac{3}{2}}}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) \left(2 e \,x^{2}-2 \sqrt{e \,x^{2}+d}\, \sqrt{e}\, x +2 d \right) a}+\frac{8 b^{2} e^{\frac{3}{2}}}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) \left(2 e \,x^{2}-2 \sqrt{e \,x^{2}+d}\, \sqrt{e}\, x +2 d \right) a^{2}}-\frac{8 b c d \sqrt{e}}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) \left(2 e \,x^{2}-2 \sqrt{e \,x^{2}+d}\, \sqrt{e}\, x +2 d \right) a^{2}}-\frac{2 \sqrt{e}\, \left(a \,c^{2} d^{2} e -b^{2} c \,d^{2} e +b \,c^{2} d^{3}+\left(a c e -b^{2} e +b c d \right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c +2 \left(4 a b \,e^{2} c -3 a \,c^{2} d e -2 b^{3} e^{2}+3 b^{2} d e c -b \,c^{2} d^{2}\right) \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)+\left(-\sqrt{e}\, x +\sqrt{e \,x^{2}+d}\right)^{2}\right)}{\left(4 a \,e^{2}-4 d e b +4 c \,d^{2}\right) a^{2} \left(\RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{3} c +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} b e -3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right)^{2} c d +8 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) a \,e^{2}-4 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) b d e +3 \RootOf \left(\textit{\_Z}^{4} c +c \,d^{4}+\left(4 b e -4 c d \right) \textit{\_Z}^{3}+\left(16 a \,e^{2}-8 d e b +6 c \,d^{2}\right) \textit{\_Z}^{2}+\left(4 b \,d^{2} e -4 c \,d^{3}\right) \textit{\_Z} \right) c \,d^{2}+b \,d^{2} e -c \,d^{3}\right)}+\frac{8 e^{2} x}{3 \sqrt{e \,x^{2}+d}\, a \,d^{3}}+\frac{2 b e x}{\sqrt{e \,x^{2}+d}\, a^{2} d^{2}}+\frac{4 e}{3 \sqrt{e \,x^{2}+d}\, a \,d^{2} x}+\frac{b}{\sqrt{e \,x^{2}+d}\, a^{2} d x}-\frac{1}{3 \sqrt{e \,x^{2}+d}\, a d \,x^{3}}"," ",0,"1/a^2*b/d/x/(e*x^2+d)^(1/2)+2/a^2*b*e/d^2*x/(e*x^2+d)^(1/2)-2/a^2*e^(1/2)/(4*a*e^2-4*b*d*e+4*c*d^2)*sum((c*(a*c*e-b^2*e+b*c*d)*_R^2+2*(4*a*b*c*e^2-3*a*c^2*d*e-2*b^3*e^2+3*b^2*c*d*e-b*c^2*d^2)*_R+a*c^2*d^2*e-b^2*d^2*e*c+b*c^2*d^3)/(_R^3*c+3*_R^2*b*e-3*_R^2*c*d+8*_R*a*e^2-4*_R*b*d*e+3*_R*c*d^2+b*d^2*e-c*d^3)*ln(-_R+(-e^(1/2)*x+(e*x^2+d)^(1/2))^2),_R=RootOf(_Z^4*c+c*d^4+(4*b*e-4*c*d)*_Z^3+(16*a*e^2-8*b*d*e+6*c*d^2)*_Z^2+(4*b*d^2*e-4*c*d^3)*_Z))-8/a*e^(3/2)/(4*a*e^2-4*b*d*e+4*c*d^2)/(2*e*x^2-2*(e*x^2+d)^(1/2)*e^(1/2)*x+2*d)*c+8/a^2*e^(3/2)/(4*a*e^2-4*b*d*e+4*c*d^2)/(2*e*x^2-2*(e*x^2+d)^(1/2)*e^(1/2)*x+2*d)*b^2-8/a^2*e^(1/2)/(4*a*e^2-4*b*d*e+4*c*d^2)/(2*e*x^2-2*(e*x^2+d)^(1/2)*e^(1/2)*x+2*d)*b*c*d-1/3/a/d/x^3/(e*x^2+d)^(1/2)+4/3/a*e/d^2/x/(e*x^2+d)^(1/2)+8/3/a*e^2/d^3*x/(e*x^2+d)^(1/2)","C"
400,0,0,223,0.086000," ","int((f*x)^m*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","\int \frac{\left(f x \right)^{m} \left(e \,x^{2}+d \right)^{q}}{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int((f*x)^m*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","F"
401,0,0,297,0.096000," ","int(x^7*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","\int \frac{x^{7} \left(e \,x^{2}+d \right)^{q}}{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int(x^7*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","F"
402,0,0,243,0.075000," ","int(x^5*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","\int \frac{x^{5} \left(e \,x^{2}+d \right)^{q}}{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int(x^5*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","F"
403,0,0,198,0.092000," ","int(x^3*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","\int \frac{x^{3} \left(e \,x^{2}+d \right)^{q}}{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int(x^3*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","F"
404,0,0,190,0.097000," ","int(x*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","\int \frac{x \left(e \,x^{2}+d \right)^{q}}{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int(x*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","F"
405,0,0,250,0.070000," ","int((e*x^2+d)^q/x/(c*x^4+b*x^2+a),x)","\int \frac{\left(e \,x^{2}+d \right)^{q}}{\left(c \,x^{4}+b \,x^{2}+a \right) x}\, dx"," ",0,"int((e*x^2+d)^q/x/(c*x^4+b*x^2+a),x)","F"
406,0,0,311,0.076000," ","int((e*x^2+d)^q/x^3/(c*x^4+b*x^2+a),x)","\int \frac{\left(e \,x^{2}+d \right)^{q}}{\left(c \,x^{4}+b \,x^{2}+a \right) x^{3}}\, dx"," ",0,"int((e*x^2+d)^q/x^3/(c*x^4+b*x^2+a),x)","F"
407,0,0,313,0.073000," ","int(x^6*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","\int \frac{x^{6} \left(e \,x^{2}+d \right)^{q}}{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int(x^6*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","F"
408,0,0,252,0.099000," ","int(x^4*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","\int \frac{x^{4} \left(e \,x^{2}+d \right)^{q}}{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int(x^4*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","F"
409,0,0,146,0.088000," ","int(x^2*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","\int \frac{x^{2} \left(e \,x^{2}+d \right)^{q}}{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int(x^2*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","F"
410,0,0,174,0.073000," ","int((e*x^2+d)^q/(c*x^4+b*x^2+a),x)","\int \frac{\left(e \,x^{2}+d \right)^{q}}{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int((e*x^2+d)^q/(c*x^4+b*x^2+a),x)","F"
411,0,0,242,0.095000," ","int((e*x^2+d)^q/x^2/(c*x^4+b*x^2+a),x)","\int \frac{\left(e \,x^{2}+d \right)^{q}}{\left(c \,x^{4}+b \,x^{2}+a \right) x^{2}}\, dx"," ",0,"int((e*x^2+d)^q/x^2/(c*x^4+b*x^2+a),x)","F"
412,0,0,303,0.096000," ","int((e*x^2+d)^q/x^4/(c*x^4+b*x^2+a),x)","\int \frac{\left(e \,x^{2}+d \right)^{q}}{\left(c \,x^{4}+b \,x^{2}+a \right) x^{4}}\, dx"," ",0,"int((e*x^2+d)^q/x^4/(c*x^4+b*x^2+a),x)","F"
413,1,101,36,0.059000," ","int((1+1/c^2/x^2)^(1/2)/(-c^4*x^4+1)^(1/2),x)","-\frac{\sqrt{\frac{c^{2} x^{2}+1}{c^{2} x^{2}}}\, \sqrt{-c^{4} x^{4}+1}\, x \,\mathrm{csgn}\left(\frac{1}{c}\right) \ln \left(\frac{2 \sqrt{-\frac{c^{2} x^{2}-1}{c^{2}}}\, c \,\mathrm{csgn}\left(\frac{1}{c}\right)+2}{c^{2} x}\right)}{\left(c^{2} x^{2}+1\right) \sqrt{-\frac{c^{2} x^{2}-1}{c^{2}}}\, c}"," ",0,"-((c^2*x^2+1)/c^2/x^2)^(1/2)*x*(-c^4*x^4+1)^(1/2)*csgn(1/c)*ln(2*(csgn(1/c)*c*(-1/c^2*(c^2*x^2-1))^(1/2)+1)/x/c^2)/(c^2*x^2+1)/(-1/c^2*(c^2*x^2-1))^(1/2)/c","C"